Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to use a nonstandard normal distribution to evaluate pregnancy and premature birth data. Here's our problem statement: The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days. Part A: Find the probability of a pregnancy lasting 309 days or longer. Part B: If the length of pregnancy is in the lowest 2%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

OK, Part A is asking us to find the probability that a pregnancy will last 309 days or longer. To do this, I'm going to use the normal distribution calculator in StatCrunch, and I know I need the normal distribution calculator because here in the problem statement it says my data is normally distributed. So the first thing I need to do is open up StatCrunch. And let's resize this window so we can see everything a little bit better.

Now in StatCrunch, I go to Stat --> Calculators --> Normal. Here in my Normal calculator, I need to establish the mean and the standard deviation, because the defaults here are for the standard Normal distribution and we have a nonstandard Normal distribution. Here in the problem statement, it says the mean is 266 days. So I need to put that in here. And the standard deviation is 15. And then I'm asked for the probability that a pregnancy will last 309 days or longer. Well, look at how this is ordered here. Probability is P, x is my random variable --- that's going to be the 309 days --- but it needs to be 309 days or longer, which means that this is greater than or equal to 309. So I got to flip that around. And notice here on the other side of the equals sign is my probability. This is a probability in decimal form. I'm asked to round to four decimal places, so I just type that in here. Fantastic!

Now in StatCrunch, I go to Stat --> Calculators --> Normal. Here in my Normal calculator, I need to establish the mean and the standard deviation, because the defaults here are for the standard Normal distribution and we have a nonstandard Normal distribution. Here in the problem statement, it says the mean is 266 days. So I need to put that in here. And the standard deviation is 15. And then I'm asked for the probability that a pregnancy will last 309 days or longer. Well, look at how this is ordered here. Probability is P, x is my random variable --- that's going to be the 309 days --- but it needs to be 309 days or longer, which means that this is greater than or equal to 309. So I got to flip that around. And notice here on the other side of the equals sign is my probability. This is a probability in decimal form. I'm asked to round to four decimal places, so I just type that in here. Fantastic!

Now, Part B asks for the number of days in which a birth would be considered premature. So babies who are born on or before how many days are considered premature? And to do that, I go back to my distribution calculator. And this is the number we're looking for now. So we get rid of that premature birth from the problem statement. We're looking for the lowest 2% of the distribution. That's the left tail of the distribution. So I need to change this to 2%. And now we just switch this around so I can get the left side and not the right side of my distribution. Now we're at the left tail of the distribution. This is the lowest 2%, and this boundary here for the tail is the value we're looking for. Rounding to the nearest integer gives me 235. Nice work!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to construct and interpret a standard deviation probability distribution with a three-number population. Here's our problem statement: Assume a population of 2, 6, and 7. Assume that samples of size n = 2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete Parts A through D below.

OK, Part A asks us to find the value of the population standard deviation, sigma. Well, that's easy enough to do. Once we put --- first, I'm going to put my samples here into StatCrunch. I don't actually need the samples to calculate the population standard deviation, but they're going to come in handy for the rest of the problem. So let's just go ahead and do that now. And I'm going to resize this window so we can see better what's going on.

To calculate the population standard deviation, I need to have the population here in the data table in StatCrunch. The population are these three numbers here listed in the problem statement --- 2, 6, and 7. So I'm going to go to this next free column here in StatCrunch, and I'm going to label this column "Population." And then I'm going to put in the actual numbers for my population: 2,6, and 7. Now I can take the standard deviation of this column to find the population standard deviation. I do that by going to Stat --> Summary Stats --> Columns.

Here in the options window, I'm going to select the column where that data is located. And then many students make the mistake of selecting this first standard deviation option here under the statistics window. The reason why that's a mistake is because this standard deviation is for samples. We're asked to calculate the population standard deviation, which means you need the unadjusted standard deviation. And to get that, you have to scroll down towards the bottom of the list here and select Unadjusted standard deviation. This is what you use when calculating standard deviation for a population. So I hit Compute!, and out comes my population standard deviation. I'm asked around to three decimal places. Good job!

To calculate the population standard deviation, I need to have the population here in the data table in StatCrunch. The population are these three numbers here listed in the problem statement --- 2, 6, and 7. So I'm going to go to this next free column here in StatCrunch, and I'm going to label this column "Population." And then I'm going to put in the actual numbers for my population: 2,6, and 7. Now I can take the standard deviation of this column to find the population standard deviation. I do that by going to Stat --> Summary Stats --> Columns.

Here in the options window, I'm going to select the column where that data is located. And then many students make the mistake of selecting this first standard deviation option here under the statistics window. The reason why that's a mistake is because this standard deviation is for samples. We're asked to calculate the population standard deviation, which means you need the unadjusted standard deviation. And to get that, you have to scroll down towards the bottom of the list here and select Unadjusted standard deviation. This is what you use when calculating standard deviation for a population. So I hit Compute!, and out comes my population standard deviation. I'm asked around to three decimal places. Good job!

Now Part B asks us to develop the probability distribution for the standard deviation of each of the nine samples. To do that, we're going to go back here to StatCrunch. And notice where the samples are actually located. They're located in rows. So the first sample is a 2 and a 2 located here in the first row. The second sample is located here in the second row. The third sample located here in the third row, and so on and so forth. So to calculate my standard deviation for these samples, I'm going to go to Stat --> Summary Stats --> Rows. Normally we select Columns, but here I'm going to select Rows because my data, the samples, are in rows.

Here in the options window, I'm going to select the columns where my sample data is located. And then I'm going to go down here under Statistics, and the statistic we're calculating is standard deviation. This is for samples, so I can select that first standard deviation there in the statistics list. And I press Compute!, and out comes a window with all of my standard deviations for each of the nine samples there in my dataset . What we're looking for is a probability distribution. So we have the numbers we need here. We just need to assemble them into a distribution.

The easiest way to do that is to sort these numbers, and I can do that very easily. If I come up here and click on the little arrow here in the title to the column in my results window, notice how everything's now sorted. And the default is to sort first by largest to --- I mean, excuse me, from lowest to highest number. If I want to start the other way, I just click again on that arrow, and now it's sorted from largest to lowest. But here in the promise statement, we see it says, “Use ascending order," which means from lowest to highest. So I'll click this again. Each time I click this, notice it's just toggling back and forth between those two settings. This is the setting I want, from lowest to highest.

So to create my distribution, I'm going to look first at the number that is listed here first. So the first number here is 0. So in this dropdown here, I'm going to select 0. And then the probability is the part over the whole. So the part is how many zeros do I have, which are three, and the whole is how many numbers do I have total, which is nine. I've got nine numbers total. Don't look at this last number and think you've got nine, because see here, everything's been sorted so it's in a different order. So I've got nine numbers total. Three is the part that they're zero. So I've got three out of nine, or three over nine, which reduces to one over three.

The next number in the dataset is the 0.7. So I'm going to select that here. How many do I have? I have two of them, so I've got two out of nine. The next number is 2.82, so I'm going to select that. I've got two of them. So that's two over nine. And then the last number 3.53, so I'm going to select that. And I have two of those --- two divided by nine. And that's really all there is to it. Well done!

Here in the options window, I'm going to select the columns where my sample data is located. And then I'm going to go down here under Statistics, and the statistic we're calculating is standard deviation. This is for samples, so I can select that first standard deviation there in the statistics list. And I press Compute!, and out comes a window with all of my standard deviations for each of the nine samples there in my dataset . What we're looking for is a probability distribution. So we have the numbers we need here. We just need to assemble them into a distribution.

The easiest way to do that is to sort these numbers, and I can do that very easily. If I come up here and click on the little arrow here in the title to the column in my results window, notice how everything's now sorted. And the default is to sort first by largest to --- I mean, excuse me, from lowest to highest number. If I want to start the other way, I just click again on that arrow, and now it's sorted from largest to lowest. But here in the promise statement, we see it says, “Use ascending order," which means from lowest to highest. So I'll click this again. Each time I click this, notice it's just toggling back and forth between those two settings. This is the setting I want, from lowest to highest.

So to create my distribution, I'm going to look first at the number that is listed here first. So the first number here is 0. So in this dropdown here, I'm going to select 0. And then the probability is the part over the whole. So the part is how many zeros do I have, which are three, and the whole is how many numbers do I have total, which is nine. I've got nine numbers total. Don't look at this last number and think you've got nine, because see here, everything's been sorted so it's in a different order. So I've got nine numbers total. Three is the part that they're zero. So I've got three out of nine, or three over nine, which reduces to one over three.

The next number in the dataset is the 0.7. So I'm going to select that here. How many do I have? I have two of them, so I've got two out of nine. The next number is 2.82, so I'm going to select that. I've got two of them. So that's two over nine. And then the last number 3.53, so I'm going to select that. And I have two of those --- two divided by nine. And that's really all there is to it. Well done!

Now Part C asks us to find the mean of the sampling distribution of a sample standard deviation. So what that means is to take these numbers that we used to create our sample sampling distribution and then find the mean of these numbers. Well, I can do that easily in StatCrunch if these numbers were listed in the data table, but they're not. They're here in an actual window. So to put them in the data table, I'm going to go back to my options window, and I'm going to check this box next to Store in data table. This will tell StatCrunch to put the results in the data table, where we can then perform further calculations on it, instead of in a separate window.

So now I've got my numbers here in the data table. And now I can just calculate the standard deviation. I go up to Stat --> Summary Stats --> Columns, select that newly created column, standard deviation for the samples, and there's my mean --- excuse me, I want this. I'm off in another world here. I want the mean, the mean of the sampling distribution. So there is my mean value for the sampling distribution, 1.571. We were asked to round to three decimal places. Fantastic!

So now I've got my numbers here in the data table. And now I can just calculate the standard deviation. I go up to Stat --> Summary Stats --> Columns, select that newly created column, standard deviation for the samples, and there's my mean --- excuse me, I want this. I'm off in another world here. I want the mean, the mean of the sampling distribution. So there is my mean value for the sampling distribution, 1.571. We were asked to round to three decimal places. Fantastic!

And now the last part, Part D asks, "Do the sample standard deviations target the value of the population standard deviation?" Sometimes these problems ask you to compare numbers. So in this case you might have been asked to compare the population value, which here is 2.16, with the mean of the sample values, which is 1.571. They don't equal to each other, and therefore we don't --- the sample doesn't target the population. The statistic doesn't target the parameter. Well, because of this, the samples that we're using here are so small, sometimes that doesn't play out quite that way. And for an unbiased estimator, you get numbers that are actually pretty much the same because you're using small samples.

So I always advise students when answering these types of questions about, you know, are your statistics targeting your parameters? Do the samples target the population? Just go by memorizing a list of biased and unbiased estimators. And we talk about those in the lecture video. So sample --- the standard deviation is going to be an unbiased estimator, so it doesn't target the population parameter. So the answer options that say that it's unbiased are going to be incorrect, because standard deviation is a biased estimator.

What did I just say? Did I just say it was unbiased? Gee, I am in another world. Standard deviation is a biased estimator. And so we want to select --- here we've got Answer option A and Answer option C. A biased estimator means that the sample does not target the population. So we're going to want to select here Answer option C. Fantastic!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>So I always advise students when answering these types of questions about, you know, are your statistics targeting your parameters? Do the samples target the population? Just go by memorizing a list of biased and unbiased estimators. And we talk about those in the lecture video. So sample --- the standard deviation is going to be an unbiased estimator, so it doesn't target the population parameter. So the answer options that say that it's unbiased are going to be incorrect, because standard deviation is a biased estimator.

What did I just say? Did I just say it was unbiased? Gee, I am in another world. Standard deviation is a biased estimator. And so we want to select --- here we've got Answer option A and Answer option C. A biased estimator means that the sample does not target the population. So we're going to want to select here Answer option C. Fantastic!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to construct and interpret a relative frequency distribution from categorical data. Here's our problem statement: Among fatal plane crashes that occurred during the past 70 years, 620 were due to pilot error, 85 were due to other human error, 308 were due to weather, 267 were due to mechanical problems, and 386 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it?

OK, I actually think this problem is a little bit easier to solve in Excel, but I'm going to solve it in StatCrunch. In StatCrunch, we're actually going to have it do everything for us. Now we can actually calculate this stuff out, and I could take my calculator and do all the old school calculations, and that's a legitimate way to approach this problem. But I'm lazy. I'm going to have StatCrunch do everything for me.

So I know it's tempting to say, "OK, we're going to make a bar plot, and we've got data here, so why don't we just press With Data?” Well, this isn't actual data. This is actually a summary of the data. We don't have the actual individual counts. We just have a summary of the counts. So because this is a summary, I'm going to select With Summary after selecting Bar Plot. The categories are the cause, and the counts are in the frequency column. I'm going to select Relative frequency. Or if I wanted to, since these are in percent form here, let's just go ahead and just select Percent. And then all we have to do is just take the numbers straight over. I'm going to tick Value above bar. This is what's going to give me the numbers that I need on my graph to put here into the answer fields in my assignment.

And that's all I need to do. Hit Compute!, and out comes this wonderful little bar graph. Now notice how that, first of all, everything's just really small as far as the typeface goes. You can barely see it. And there's actually a zoom feature that we can use. But first I want to make sure that we get this in the right order, which I didn't do previously. So back in my options menu, I need to make sure I order by worksheet. And that way it'll put in the same order that we have here in our assignment.

Now I've got this ordered correctly. Now to get the zoom feature, there's these three bars that you see here in the lower left. Go ahead and click on that, and then hit Zoom. And now, when I click on the zoom tool, I can zoom in on area, I can move this around, and now there's the number I need to put in for pilot error, 37.2. I hit the X to go back. Whoops, that's not what I wanted to do. I want to go back this way. And now I just go ahead and just do the same thing for each of the following categories. And it really is that simple.

Now to do this the old school way, I'd have to take the sum of the numbers that are listed here, and I could do that easily enough in StatCrunch. And then once I have that sum, I go ahead and divide by the --- each of these counts by the total sum, and that gives me the same percentages that you'll see here. And I can show you that in a moment as soon as I get done with all of this business. So we've got two more numbers to put in. I'm going to put that in here. And we've got one more. Excellent!

Now to illustrate what I was showing you before, just very quickly, if you go up to Stat --> Summary stats --> Columns, at the frequency, we want to get the sum. The sum is 1666. So if I take that 1666 and divide it into each one of these numbers, I'm going to get the same numbers out. So if I took the first number, 620 for pilot error, and I divided by 1666, notice we get the same 37.2% that is the correct answer. And we can do the same thing for each of the others in succession. But like I said, I'm lazy. I just let StatCrunch do all that calculating for me.

So I know it's tempting to say, "OK, we're going to make a bar plot, and we've got data here, so why don't we just press With Data?” Well, this isn't actual data. This is actually a summary of the data. We don't have the actual individual counts. We just have a summary of the counts. So because this is a summary, I'm going to select With Summary after selecting Bar Plot. The categories are the cause, and the counts are in the frequency column. I'm going to select Relative frequency. Or if I wanted to, since these are in percent form here, let's just go ahead and just select Percent. And then all we have to do is just take the numbers straight over. I'm going to tick Value above bar. This is what's going to give me the numbers that I need on my graph to put here into the answer fields in my assignment.

And that's all I need to do. Hit Compute!, and out comes this wonderful little bar graph. Now notice how that, first of all, everything's just really small as far as the typeface goes. You can barely see it. And there's actually a zoom feature that we can use. But first I want to make sure that we get this in the right order, which I didn't do previously. So back in my options menu, I need to make sure I order by worksheet. And that way it'll put in the same order that we have here in our assignment.

Now I've got this ordered correctly. Now to get the zoom feature, there's these three bars that you see here in the lower left. Go ahead and click on that, and then hit Zoom. And now, when I click on the zoom tool, I can zoom in on area, I can move this around, and now there's the number I need to put in for pilot error, 37.2. I hit the X to go back. Whoops, that's not what I wanted to do. I want to go back this way. And now I just go ahead and just do the same thing for each of the following categories. And it really is that simple.

Now to do this the old school way, I'd have to take the sum of the numbers that are listed here, and I could do that easily enough in StatCrunch. And then once I have that sum, I go ahead and divide by the --- each of these counts by the total sum, and that gives me the same percentages that you'll see here. And I can show you that in a moment as soon as I get done with all of this business. So we've got two more numbers to put in. I'm going to put that in here. And we've got one more. Excellent!

Now to illustrate what I was showing you before, just very quickly, if you go up to Stat --> Summary stats --> Columns, at the frequency, we want to get the sum. The sum is 1666. So if I take that 1666 and divide it into each one of these numbers, I'm going to get the same numbers out. So if I took the first number, 620 for pilot error, and I divided by 1666, notice we get the same 37.2% that is the correct answer. And we can do the same thing for each of the others in succession. But like I said, I'm lazy. I just let StatCrunch do all that calculating for me.

The next part of the problem asks, “What is the most serious threat to aviation safety, and can anything be done about it?" Well, the most serious threat is going to be the category with the largest percentile. And that's going to be the 37.2% related to pilot error. Can you do something about pilot error? Yeah, you could probably train your pilots better. So let's see, we got --- yeah, right here, Answer option D: "Pilot errors are the most serious threat. Pilots could be better trained." So I go ahead and select that one. Excellent!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below, and let us know how good a job we did or how we can improve. And if your stats teacher is boring, or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below, and let us know how good a job we did or how we can improve. And if your stats teacher is boring, or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to determine the appropriate level of measurement for Olympic years. Here's our problem statement: Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below: Years in which an Olympics was held.

OK, we're given four different answer options here, each one corresponding to the different levels of measurement. And what's interesting here is that we've got definitions of each of the different levels to help us select the right answer. So we look at the definitions here --- the ordinal level of measurement --- and this says that "the data can be ordered but differences cannot be found or are meaningless." Well, we can find differences between different years, so that's obviously not going to be the right answer. "The nominal level of measurement is most appropriate because the data cannot be ordered." Well, yeah, the data actually can be ordered. That's the whole point of having years. We can order them from low to high or high to low.

That's the interval level of measurement. It "is most appropriate because the data can be ordered" --- that's true. "Differences can be found and are meaningful" --- that's true. And "there's no natural starting zero point" --- that's true. The zero point for years is just an arbitrarily chosen value, so it's just something that's accepted by convention. There's no natural point for zero, and so the interval level of measurement is what we have. And when you see years, you need to think interval level of measurement because the two pretty much go together. The final answer --- ratio level of measurement --- would not be correct because it says here "the data can be ordered," which is true. "Differences can be found or are meaningful" --- that's true. "There is a natural starting point," and that's what we don't have with the years. So the correct answer here is the interval level of measurement. Fantastic!

That's the interval level of measurement. It "is most appropriate because the data can be ordered" --- that's true. "Differences can be found and are meaningful" --- that's true. And "there's no natural starting zero point" --- that's true. The zero point for years is just an arbitrarily chosen value, so it's just something that's accepted by convention. There's no natural point for zero, and so the interval level of measurement is what we have. And when you see years, you need to think interval level of measurement because the two pretty much go together. The final answer --- ratio level of measurement --- would not be correct because it says here "the data can be ordered," which is true. "Differences can be found or are meaningful" --- that's true. "There is a natural starting point," and that's what we don't have with the years. So the correct answer here is the interval level of measurement. Fantastic!

Let's go through one more example just to illustrate what we've got here. So now we've got the number of houses that people own. Well, the number of houses people own, would that be the ratio level of measurement? Yeah, probably, because look, the data can be ordered, the differences can be found and are meaningful. I mean, you've got one person who's got two houses, and one person's got one. That extra house --- that's a meaningful difference. There is a natural starting zero point. It's like you got zero houses. That's a natural place to start counting something. So ratio level of measurement is what we would select here. Fantastic!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below, and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below, and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to perform mean hypothesis testing on the number of words per page. Here's our problem statement: A simple random sample of 10 pages from a dictionary is obtained. The number of words defined on those pages are found with the results: n = 10, x-bar = 55.3 words, s = 16.6 words. Given that this dictionary has 1,456 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.1 words. Use a 0.05 significance level to test the claim that the mean number of words per page is greater than 48.1 words. What does the results suggest about the claim that there are more than 70,000 defined words, identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. Assume that the population is normally distributed.

OK, the first part of this problem asks us for the null and alternative hypotheses. The null hypothesis is by definition a statement of equality, so Answer option C is not going to be the right answer because this null hypothesis is not a statement of equality. Of the three answer options that remain, let's look at our alternative hypothesis. And normally we get that from the claim. The claim here from our problem statement --- well, there's two claims: There's an original claim, and then there's a modified claim. And it looks like we're going to be using the modified claim to define our null and alternative hypothesis. And that is that the mean number of words per page is greater than 48.1 words. So we take the one that says greater than 48.1. And here it is right here, Answer option B. Nice work!

OK, the second part of this problem asks us for the test statistic . And to find the test statistic, we're going to pop out StatCrunch. So I'll take this window, and I'm going to resize it so that we can see better what's going on here. OK, inside StatCrunch, I go to Stat --> T Stats (because I don't know the population standard deviation) --> One Sample (because we have just the one sample) --> With Summary (because we don't have any actual data). Here in the options window, I need to put in my sample statistics from the problem statement. We have those right here, so I'm just going to take that information and stick it in here. The sample mean is x-bar; that's the 53 --- excuse me, 55.3. And then the sample standard deviation is going to be s; that's the 16.6. Sample size is going to be n, and that's 10.

Check for this radio button for Hypothesis test. That's the default selection. We want to keep that because we're performing a hypothesis test. We want to make sure this area matches what we selected here in the previous part of the problem. So we need to change this claimed value from zero to 48.1. And then I need to make sure that this inequality sign matches what we have over here for our alternative hypothesis. And now I've got everything I need. I press Compute!, and here in my results window, the second to last value is the test statistic. I'm asked to round to two decimal places. Excellent!

Check for this radio button for Hypothesis test. That's the default selection. We want to keep that because we're performing a hypothesis test. We want to make sure this area matches what we selected here in the previous part of the problem. So we need to change this claimed value from zero to 48.1. And then I need to make sure that this inequality sign matches what we have over here for our alternative hypothesis. And now I've got everything I need. I press Compute!, and here in my results window, the second to last value is the test statistic. I'm asked to round to two decimal places. Excellent!

Now the next part of the problem asks for the P-value. We've already done all the work to calculate it. Look back here at the results window. It's that last value there in the table, right next door to our test statistic. We're asked to round to three decimal places. Nice work!

And now the last part of this problem asks us to state the final conclusion. To do this, we're going to compare our P-value with our significance level we have here in the problem statement. It says, "Use a 5% significance level." Here, we've got a P-value of over 10%. 10% is well above 5%, so we're outside the region of rejection. And when you're outside the region of rejection, you fail to reject the null hypothesis. Every time you fail to reject, there is not sufficient evidence. And here our original claim was that there was more than 70,000 defined words. Excellent!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to distinguish an observational study from an experiment. Here's our problem statement: Determine whether the description corresponds to an observational study or experiment. Research is conducted to determine if there is a relation between Parkinson's disease and childhood head trauma. Does the description correspond to an observational study or an experiment?

OK, the key difference between an observational study and an experiment is that an observational study is just what the name says. You're just looking at what's there. You're just observing. You're not actually . . . you're not inserting anything, any sort of change, into the variables that you're looking at. An experiment, on the other hand, requires a treatment. There's something that you're doing so that you can observe a change in what you're observing here.

The problem statement says that research is being conducted, and a lot of people, when they think about research, they think about that. Especially when you're dealing with medical things, they associate that with experiments because they're thinking about some sort of drug testing, or we're testing out some sort of procedure to treat the disease. But in reality here, look at what's actually being said in the statement. There's nothing in here that says anything about a treatment. It just says research is conducted. Well, for all we know, that could mean all we're doing is simply collecting data from people who have Parkinson's disease and seeing which of them had childhood head trauma. And then we're taking that data and running a statistical analysis to see if there's a correlation between those two variables. That is actual research that could be conducted. So we don't know what's going on here. And there's no indication that there's a treatment going on here.

So this doesn't qualify as an experiment. This qualifies as an observational study because, again, there is no treatment here. We're just taking the people who have Parkinson's disease and seeing if they had childhood head trauma. We're just looking to see what's there. We're not actually inserting any sort of treatment to observe any sort of change. Excellent!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>The problem statement says that research is being conducted, and a lot of people, when they think about research, they think about that. Especially when you're dealing with medical things, they associate that with experiments because they're thinking about some sort of drug testing, or we're testing out some sort of procedure to treat the disease. But in reality here, look at what's actually being said in the statement. There's nothing in here that says anything about a treatment. It just says research is conducted. Well, for all we know, that could mean all we're doing is simply collecting data from people who have Parkinson's disease and seeing which of them had childhood head trauma. And then we're taking that data and running a statistical analysis to see if there's a correlation between those two variables. That is actual research that could be conducted. So we don't know what's going on here. And there's no indication that there's a treatment going on here.

So this doesn't qualify as an experiment. This qualifies as an observational study because, again, there is no treatment here. We're just taking the people who have Parkinson's disease and seeing if they had childhood head trauma. We're just looking to see what's there. We're not actually inserting any sort of treatment to observe any sort of change. Excellent!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to use a binomial distribution to evaluate toy manufacturing quality control. Here's our problem statement: When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 35 batteries and determine whether each is within specifications. The entire shipment is accepted if at most three batteries do not meet specifications . A shipment contains 3000 batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all shipments be accepted, or will many be rejected?

OK, the first part of this problem is asking us to calculate the probability that the whole shipment will be accepted. And to do that, we're going to use the binomial distribution calculator in StatCrunch. So first we need to pull up StatCrunch, and I can do that here. I'm going to pop this window out, and then I'm going to resize it so we can see a little bit better everything that's going on here. Then inside StatCrunch, I'll go to Stat --> Calculators --> Binomial.

Here in my binomial calculator, I need to add in parameters of my distribution. The sample size is 35 batteries. Why am I using the 35 and not the 3000? Well, because 3000 is the population. 3000 is the entire shipment. We're just taking a portion of that population. That's what a sample is --- a portion of the population. So the 35 batteries is our sample size and not the 3000. Probability of success? Well, we're going to define success as not meeting specifications, and we do that because it just works out better that way. I know it sounds funky that, you know, not meeting specifications is going to be a success, but it just makes the problem easier. The percentage is 2% of the population aren't meeting specifications, so that's the probability of success.

Then we have to look to see that the entire shipment will be accepted if that most three batteries do not meet specifications. So we can have no batteries, or one battery, or two battery, or three batteries, and that would mean that we are accepting the shipment. So here we're actually calculating the probability based on one number, but we need four different numbers: 0, 1, 2, and 3. So I'm going to come up here and press the Between option on my calculator so I can put in everything between zero and three. And there we would get our probability, 0.9948918. We were asked to round to four decimal places. So that comes out to be 0.9949. Nice work!

Here in my binomial calculator, I need to add in parameters of my distribution. The sample size is 35 batteries. Why am I using the 35 and not the 3000? Well, because 3000 is the population. 3000 is the entire shipment. We're just taking a portion of that population. That's what a sample is --- a portion of the population. So the 35 batteries is our sample size and not the 3000. Probability of success? Well, we're going to define success as not meeting specifications, and we do that because it just works out better that way. I know it sounds funky that, you know, not meeting specifications is going to be a success, but it just makes the problem easier. The percentage is 2% of the population aren't meeting specifications, so that's the probability of success.

Then we have to look to see that the entire shipment will be accepted if that most three batteries do not meet specifications. So we can have no batteries, or one battery, or two battery, or three batteries, and that would mean that we are accepting the shipment. So here we're actually calculating the probability based on one number, but we need four different numbers: 0, 1, 2, and 3. So I'm going to come up here and press the Between option on my calculator so I can put in everything between zero and three. And there we would get our probability, 0.9948918. We were asked to round to four decimal places. So that comes out to be 0.9949. Nice work!

And now the second part has a few different fields for us to fill in. The first is asking for an acceptance rate. And we have that acceptance rate right here. We just calculated it. It's in decimal form. We need to convert it to percent form. And we do that by moving the decimal place over two places. So that becomes 99.49. And then the rejection rate is just a complement of the acceptance rate. So if we subtract that from 100 and I can do that with my handy dandy calculator here, just subtract that out from 100. And that gives me my rejection rate, which is awfully low. So we've got some good stuff going on here because it was such a low rejection rate. It's going to be that almost all the shipments are going to be accepted. Fantastic!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to construct a relative frequency distribution from a frequency events table in StatCrunch. Here's our problem statement: Construct one table that includes relative frequencies based on the frequency distribution shown below. Then compare the amounts of tar in non-filtered and filtered cigarettes. Do the cigarette filters appear to be effective? (Hint: the filters reduce the amount of tar ingested by the smoker.)

OK, the first part of this problem asks us for our relative frequency distributions. And to do that, we need to take a look at the data that's being provided. So here's the data. We're going to dump this in StatCrunch. I've actually worked this problem out before in a previous post and video showing you how to do this in Excel, because I think Excel is a little bit quicker with this. But I got a request to do this in StatCrunch, and so here we go. Today I'm going to download this data here into StatCrunch.

OK, here's my data in StatCrunch, and now I'm going to resize this window a bit so we can get a better view of everything that's going on. Great. OK, so in StatCrunch, to make a relative frequency distribution, you want to make the graphical portion. Go to Graph --> Bar Plot --> With Summary. It might be tempting to come down here and select Histogram, but you don't want to do that because that's not going to give you what you need. You want to go up here to Bar Plot, and then you want to select With Summary because the data that we're given are frequency counts and not the actual data themselves.

Here in my options window, I'm going to select my categories. So the first one that I make is for the non-filtered cigarettes, and then I select its frequency for the counts. Down here under Type, it will be tempting to select Relative Frequency. But this is actually going to give you a number in decimal form. And notice here in your assignment, you're asked for percentages. So we want to click on Percent under Type.

And then under Order By, we want to make sure that we select Worksheet. What this does is it gives us the columns in our relative frequency distribution according to the order that's in the worksheet. We don't want to do it by, you know, whether the values are Counts Ascending or Descending. We want it as the order of the worksheet because that's going to match the order of the categories here in our assignment. And then the real kicker right here --- check this box next to Value above bar. This will give us the numbers that we need to stick into our answer fields here in our assignment.

Once I've done that, I hit Compute!, e viola! Here we have our relative frequency distribution. And the numbers on the tops of the bars represent the percentages that form our relative frequency distribution. So now all I've got to do is just match up the columns here with the columns here and take the numbers straight off the top. So first we have 4 - 7. There's no column for that here, so I'm just going to press zero. 8 - 11 — similarly, there's nothing there. 12 - 15 — there's a 4. And you see I'm just coming down here and just taking that number off the top. If there's no column there, then obviously the number I need to put in is zero. And I just do it one after the other, and eventually that gets me everything I need for that.

Now I need to go and do the same thing for the non-filtered --- actually that was the non-filtered. Now I do the same thing for the filtered cigarettes. I could just come in here into my options window and change everything up. But I know further on down the problem --- see here, it says, "Do the cigarette filters appear to be effective?" I'm going to have to compare the two graphs in order to get the answer to that question. So I'm going to make a separate graph. So just come in, and look at the same menu options I did before. Well, this time I'm going to select the filtered cigarettes, and you can see I'm selecting the same options there that I did before.

OK, here's my new graph. And now I'm going to fill in the numbers here from those actual columns and make sure everything matches up. And then that's the last column there. So the rest of these are going to be zero. So I'll go ahead and put that in here. And I check my answer. Excellent!

OK, here's my data in StatCrunch, and now I'm going to resize this window a bit so we can get a better view of everything that's going on. Great. OK, so in StatCrunch, to make a relative frequency distribution, you want to make the graphical portion. Go to Graph --> Bar Plot --> With Summary. It might be tempting to come down here and select Histogram, but you don't want to do that because that's not going to give you what you need. You want to go up here to Bar Plot, and then you want to select With Summary because the data that we're given are frequency counts and not the actual data themselves.

Here in my options window, I'm going to select my categories. So the first one that I make is for the non-filtered cigarettes, and then I select its frequency for the counts. Down here under Type, it will be tempting to select Relative Frequency. But this is actually going to give you a number in decimal form. And notice here in your assignment, you're asked for percentages. So we want to click on Percent under Type.

And then under Order By, we want to make sure that we select Worksheet. What this does is it gives us the columns in our relative frequency distribution according to the order that's in the worksheet. We don't want to do it by, you know, whether the values are Counts Ascending or Descending. We want it as the order of the worksheet because that's going to match the order of the categories here in our assignment. And then the real kicker right here --- check this box next to Value above bar. This will give us the numbers that we need to stick into our answer fields here in our assignment.

Once I've done that, I hit Compute!, e viola! Here we have our relative frequency distribution. And the numbers on the tops of the bars represent the percentages that form our relative frequency distribution. So now all I've got to do is just match up the columns here with the columns here and take the numbers straight off the top. So first we have 4 - 7. There's no column for that here, so I'm just going to press zero. 8 - 11 — similarly, there's nothing there. 12 - 15 — there's a 4. And you see I'm just coming down here and just taking that number off the top. If there's no column there, then obviously the number I need to put in is zero. And I just do it one after the other, and eventually that gets me everything I need for that.

Now I need to go and do the same thing for the non-filtered --- actually that was the non-filtered. Now I do the same thing for the filtered cigarettes. I could just come in here into my options window and change everything up. But I know further on down the problem --- see here, it says, "Do the cigarette filters appear to be effective?" I'm going to have to compare the two graphs in order to get the answer to that question. So I'm going to make a separate graph. So just come in, and look at the same menu options I did before. Well, this time I'm going to select the filtered cigarettes, and you can see I'm selecting the same options there that I did before.

OK, here's my new graph. And now I'm going to fill in the numbers here from those actual columns and make sure everything matches up. And then that's the last column there. So the rest of these are going to be zero. So I'll go ahead and put that in here. And I check my answer. Excellent!

Now the second part of this problem asks, "Do cigarette filters appear to be effective?" Well, as I just mentioned a moment ago, I'm going to have to compare my graphs to get that. So let's move this down here a little bit and then we're going to do the same thing here. And then I'm going to slide this up above the other one, but we're gonna move it over so that we match columns up. So now I've got 12 - 15; here's my first column. I'm going to match this up to 12 - 15 here.

So now I've got a better picture of what's going on. And we notice here on the horizontal axis of our graphs, we're looking at the amount of tar in the cigarettes. So here are the non-filtered, here are the filtered, and it looks like for the higher tar levels, the non-filtered cigarettes seem to be capturing that out. And the filtered cigarettes? Not so much so.

So would I say that do they appear to be effective? Yeah, because the higher tar (what you're trying to get out then) that, you know, the non-filtered cigarettes --- of course, they're letting all that stuff through. But the filtered cigarettes, they're actually capturing a lot of that stuff, and you don't see the higher tar levels for the filtered cigarettes. So it does appear that the filters are working in the cigarettes; they are effective. So I come over here and select the answer option that matches that. Excellent!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

]]>So now I've got a better picture of what's going on. And we notice here on the horizontal axis of our graphs, we're looking at the amount of tar in the cigarettes. So here are the non-filtered, here are the filtered, and it looks like for the higher tar levels, the non-filtered cigarettes seem to be capturing that out. And the filtered cigarettes? Not so much so.

So would I say that do they appear to be effective? Yeah, because the higher tar (what you're trying to get out then) that, you know, the non-filtered cigarettes --- of course, they're letting all that stuff through. But the filtered cigarettes, they're actually capturing a lot of that stuff, and you don't see the higher tar levels for the filtered cigarettes. So it does appear that the filters are working in the cigarettes; they are effective. So I come over here and select the answer option that matches that. Excellent!

And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.

Howdy! Welcome to Aspire Mountain Academy. I am Professor Curtis, your instructor for Stat 101. And as I promised in the last video, we were going to show you how to look for a specific Homework Help video. In the last video we looked at different resources that we have that are free and available to everyone to help them with their statistics courses. And now we're going to look at how do you find a specific homework help video. There's two ways to do that. You can go through the website, or you can go through the YouTube channel.

Let's take a look first at the website. If I pull up my browser here, and I'm gonna go to aspiremountainacademy.com. So here we are at Aspire Mountain Academy. And if I go to Courses and then scroll down here, click on the statistics course, and now you see here I've got two different links here --- one for Homework Help and one for Problem Index. If you're looking for a specific problem, the first place you want to go to is the Problem Index.

So here I'm going to scroll down. And look, you've got this table here that shows you all the problems, and they're organized by problem ID number. The problem ID number is located in the top left corner of your assignment window. If I go here, click on this first one, the problem ID number was 1.1.30, and look here. Here in the video, see up here at the top left corner of that homework window there in your assignment, 1.1.30. So if you're looking for a specific homework problem, a quick way to do that is just come here to the website and use the list there.

So here I'm going to scroll down. And look, you've got this table here that shows you all the problems, and they're organized by problem ID number. The problem ID number is located in the top left corner of your assignment window. If I go here, click on this first one, the problem ID number was 1.1.30, and look here. Here in the video, see up here at the top left corner of that homework window there in your assignment, 1.1.30. So if you're looking for a specific homework problem, a quick way to do that is just come here to the website and use the list there.

Now some students, they actually prefer to just stay in YouTube, because you can see these videos here are connected to YouTube. So let's go to YouTube, and I'll show you how to find a specific Homework Help video.

OK, so let's look for that same homework problem that we we're looking at just now in the blog. So if I type in "aspire mountain academy" and then I type in that problem ID number "1.1.30", notice what comes up here. You've got this guy --- I don't know who he is, but he's got a playlist, and he calls it "Aspire Mountain Academy". And because of that, he's getting all the traffic from the work that I'm doing. So I'm doing my work here. All he's doing is taking my work and putting it into a different package and he, because you know it comes up first here in the list of search results, people are clicking on it. And we don't want to be supporting people who aren't doing the actual work. So let's not give this guy any more of the traffic that rightfully belongs to Aspire Mountain Academy.

So I'm going to click here on the channel. Actually I probably could've just clicked on that actual link there. But here in the channel I can also search for a video if I just go to this search field and type in that problem ID number. Well, ah, here it is --- the actual video. And you can click on it and watch it. And that's pretty much the way it goes. You could also find that same video if I were to go to a playlist. So that was Section 1.1, so if I scroll down looking for --- yep, here's Homework Help videos for section 1.1. So if I go to the full playlist, so far we've only got two problems from that first section. But again, it's not a section that we get a lot of requests for doing videos for.

If you are looking for a specific homework problem, and you don't find it here on the site, you can request it. And there's different ways to do that. You can --- if you're in the blog you can just put a comment on the blog. A lot of students that are using YouTube, they'll just post it in a comment to whatever video they were watching. The other place you can do it is in the discussion forum. So if I go back to the channel page and come up here to Discussion, there's nothing posted here yet, but this is another great place for you to request a video.

And remember when you're requesting your video, don't just type in the words from the problem, because there's literally hundreds of statistics problems that are there in your course in MyMathLab. So it's really hard for us to figure out where that problem is if you just type in the words from the problem statement. It's a lot easier for us to find it if you use that problem ID number. So request a problem that you want to see worked out with the problem ID number. And we actually honor those requests. We'll make a video, post it up here on the site, and get back to you.

So that's pretty much how you look for a specific Homework Help video with the resources that we have at Aspire Mountain Academy. We hope you found this video helpful. You could find more videos for this and other courses at aspiremountainacademy.com. Thanks for watching! And we'll see you in the next video.

]]>OK, so let's look for that same homework problem that we we're looking at just now in the blog. So if I type in "aspire mountain academy" and then I type in that problem ID number "1.1.30", notice what comes up here. You've got this guy --- I don't know who he is, but he's got a playlist, and he calls it "Aspire Mountain Academy". And because of that, he's getting all the traffic from the work that I'm doing. So I'm doing my work here. All he's doing is taking my work and putting it into a different package and he, because you know it comes up first here in the list of search results, people are clicking on it. And we don't want to be supporting people who aren't doing the actual work. So let's not give this guy any more of the traffic that rightfully belongs to Aspire Mountain Academy.

So I'm going to click here on the channel. Actually I probably could've just clicked on that actual link there. But here in the channel I can also search for a video if I just go to this search field and type in that problem ID number. Well, ah, here it is --- the actual video. And you can click on it and watch it. And that's pretty much the way it goes. You could also find that same video if I were to go to a playlist. So that was Section 1.1, so if I scroll down looking for --- yep, here's Homework Help videos for section 1.1. So if I go to the full playlist, so far we've only got two problems from that first section. But again, it's not a section that we get a lot of requests for doing videos for.

If you are looking for a specific homework problem, and you don't find it here on the site, you can request it. And there's different ways to do that. You can --- if you're in the blog you can just put a comment on the blog. A lot of students that are using YouTube, they'll just post it in a comment to whatever video they were watching. The other place you can do it is in the discussion forum. So if I go back to the channel page and come up here to Discussion, there's nothing posted here yet, but this is another great place for you to request a video.

And remember when you're requesting your video, don't just type in the words from the problem, because there's literally hundreds of statistics problems that are there in your course in MyMathLab. So it's really hard for us to figure out where that problem is if you just type in the words from the problem statement. It's a lot easier for us to find it if you use that problem ID number. So request a problem that you want to see worked out with the problem ID number. And we actually honor those requests. We'll make a video, post it up here on the site, and get back to you.

So that's pretty much how you look for a specific Homework Help video with the resources that we have at Aspire Mountain Academy. We hope you found this video helpful. You could find more videos for this and other courses at aspiremountainacademy.com. Thanks for watching! And we'll see you in the next video.

Howdy! Welcome to Aspire Mountain Academy. And in this video we're going to look at an introduction to some of the free course resources that are available to statistic students. And we're going to start by looking at StatCrunch.

So in the lecture videos that we're currently producing, we reference data sets in StatCrunch. So if I bring up my browser here and I can show you, here is the group for the Stat 101 course in Aspire Mountain Academy. And if you want to join this group, anyone can join this group. There's no need to wait for an administrator to let you in. You join the group and boom! You're in.

And the way you find the group is once you log into StatCrunch, come over here to Explore (or you can touch this little arrow next to it and you want to go to groups) or I can just hit Explore and then again hit Groups. So there's all these different groups that you see come up. And then in the search box here, I want to look for Aspire Mountain Academy. And look at this. Here we go. You click on it. And then you'll have a --- there'll actually be a link up here where you can actually join up with the group. And so you just click the link, join the group, and you're in. So for those of you who --- once the lecture videos come out, for those of you who are interested in this resource is here and available for you, again, free of charge.

And the way you find the group is once you log into StatCrunch, come over here to Explore (or you can touch this little arrow next to it and you want to go to groups) or I can just hit Explore and then again hit Groups. So there's all these different groups that you see come up. And then in the search box here, I want to look for Aspire Mountain Academy. And look at this. Here we go. You click on it. And then you'll have a --- there'll actually be a link up here where you can actually join up with the group. And so you just click the link, join the group, and you're in. So for those of you who --- once the lecture videos come out, for those of you who are interested in this resource is here and available for you, again, free of charge.

There are other resources that are available. So first let me sign out of StatCrunch. And let's go to the companion website, aspiremountainacademy.com, and here if I click on Courses, I can scroll down to get to the statistics class. The course offering list is really short right now, but that's because we're still in production of a whole bunch of other classes, so be sure to stay tuned for that. But click here on the title; it's a link. It takes me into the page for that course. And of course, as I said, the lecture videos are still in beta production. Not quite done yet, but we're almost there, so be sure to hang tight for that. We have homework help videos and then an index where you can actually look at different --- searching for specific problems that you want to find. And that would be great for a lot of students.

What I want to show you is coming into Homework Help. And it's essentially a blog where we've got videos showing you how to work each individual homework problem. And of course if you don't, if you'd rather read rather than watch the video, we've got the text here down below. So that's always helpful. And then you notice that I put my mouse over here, you know, and this is coming up as a YouTube video. This is actually linked to YouTube. We have a YouTube channel. So let me actually go out to YouTube and show you what we have here.

What I want to show you is coming into Homework Help. And it's essentially a blog where we've got videos showing you how to work each individual homework problem. And of course if you don't, if you'd rather read rather than watch the video, we've got the text here down below. So that's always helpful. And then you notice that I put my mouse over here, you know, and this is coming up as a YouTube video. This is actually linked to YouTube. We have a YouTube channel. So let me actually go out to YouTube and show you what we have here.

So here we are on YouTube. The first thing I want to do is find the Aspire Mountain Academy channel. So if I go to "aspire mountain academy" --- oh look, this comes up. And notice what I have here in my search results. So this first hit right here is actually somebody who --- I don't know who this is, but this individual has essentially made a playlist of the content on Aspire Mountain Academy. And then, they've actually put this up here, and they're listed first because they've got tons more hits. So what this guy is actually doing --- I don't know, again, I don't know who this guy is, but this guy has taken the content that I've been posting here on Aspire Mountain Academy, and he's been repackaging it and then getting all the traffic. So let's not support people who aren't doing the actual work. Let's support people who are doing the actual work.

So if I click on the channel name here, you can see this is the name of the channel: AspireMtnAcademy. And we have here a list of videos. So if I click on Videos, I can see all the different videos that have been posted to the channel. And you can see there's a ton of stuff here. So lots of help for students who are struggling with their homework assignments. You can come over here to Playlists. We now have playlists here at Aspire Mountain Academy. They were requested by students. And so we've worked hard to put them together. And, if you're interested in watching videos in a playlist format, just come here and you can find the playlist that's --- notice how the names of the playlists correspond with individual sections of the course. So just find the one for the section that you're working on and then hit Play All, and it'll come up for you.

If I want, I can actually look at specific --- and let's just look at this one. So here the playlist is actually starting, and we don't need to have that going. So yeah, you can see here the playlists are going and can actually --- if I wanted to, I could go back --- look at this! --- and actually view the full playlist. And so here we go. Ooh, look at that. Lots of stuff to look at. So here are the videos that are currently in this playlist right here. But you know, like I said, we're going to continue to add videos, and so every time we add a new video, we'll put it in its proper playlist. So every time you come here, you always have the most up-to-date playlists for the videos that are on Aspire Mountain Academy. Again, there's no need to go anywhere else. We've got everything you need right here.

So if I click on the channel name here, you can see this is the name of the channel: AspireMtnAcademy. And we have here a list of videos. So if I click on Videos, I can see all the different videos that have been posted to the channel. And you can see there's a ton of stuff here. So lots of help for students who are struggling with their homework assignments. You can come over here to Playlists. We now have playlists here at Aspire Mountain Academy. They were requested by students. And so we've worked hard to put them together. And, if you're interested in watching videos in a playlist format, just come here and you can find the playlist that's --- notice how the names of the playlists correspond with individual sections of the course. So just find the one for the section that you're working on and then hit Play All, and it'll come up for you.

If I want, I can actually look at specific --- and let's just look at this one. So here the playlist is actually starting, and we don't need to have that going. So yeah, you can see here the playlists are going and can actually --- if I wanted to, I could go back --- look at this! --- and actually view the full playlist. And so here we go. Ooh, look at that. Lots of stuff to look at. So here are the videos that are currently in this playlist right here. But you know, like I said, we're going to continue to add videos, and so every time we add a new video, we'll put it in its proper playlist. So every time you come here, you always have the most up-to-date playlists for the videos that are on Aspire Mountain Academy. Again, there's no need to go anywhere else. We've got everything you need right here.

One final thing that I want to point out. Let's go back to the --- let's see here. Yeah, let's just go with the back button. So if I go back here, and I go to Discussion under the channel name. Now, there's no discussion here. Nobody started anything yet. But this is a good place to go if you have a comment you want to make, give us some feedback on things you like, things that you'd like to see. We've had students in the past who have made comments to the blog on the website and also to individual videos here on YouTube. And they, you know, occasionally will request something. And so if you want to request something, that's --- this is a great place to do it. Make sure that you use the problem ID number.

If you're looking for a specific video and you don't find it here on the site, you can request that we do the video to walk you through the homework problem. So the place to do that is right here, or you could just do it as, you know, a comment on the actual video itself, but make sure you get the problem ID number. I've had students who start typing out the actual problem that they see in their assignment window, like what you see right here. If I go back here --- oops, let's blow this out. Let's go back. So if I go back to a video, this is --- go to this first one. We don't need that. But notice there's a number up here at the top left corner of your screen. This is a problem ID number. And this is what you're going to need to request a video. If you don't see a video here in our channel and you want us to actually make one, then this is how you request it. Take this ID number that you see up at the top and request the problem that you want us with this ID number. And that will help us to identify very quickly the problem you're looking at. And we'll show you how to go through it step by step in a new video that we'll make for you.

So that's pretty much all we got for this video. I hope you found it helpful. Again, let us know in the comments below if you'd like to see anything new, or if, you know, if we did a good job, tell us that too. We'd love to get feedback from the people that we're trying to help. And keep in mind, you can find more videos for this and other courses at aspiremountainacademy.com. Thanks for watching! And I'll see you in the next video.

]]>If you're looking for a specific video and you don't find it here on the site, you can request that we do the video to walk you through the homework problem. So the place to do that is right here, or you could just do it as, you know, a comment on the actual video itself, but make sure you get the problem ID number. I've had students who start typing out the actual problem that they see in their assignment window, like what you see right here. If I go back here --- oops, let's blow this out. Let's go back. So if I go back to a video, this is --- go to this first one. We don't need that. But notice there's a number up here at the top left corner of your screen. This is a problem ID number. And this is what you're going to need to request a video. If you don't see a video here in our channel and you want us to actually make one, then this is how you request it. Take this ID number that you see up at the top and request the problem that you want us with this ID number. And that will help us to identify very quickly the problem you're looking at. And we'll show you how to go through it step by step in a new video that we'll make for you.

So that's pretty much all we got for this video. I hope you found it helpful. Again, let us know in the comments below if you'd like to see anything new, or if, you know, if we did a good job, tell us that too. We'd love to get feedback from the people that we're trying to help. And keep in mind, you can find more videos for this and other courses at aspiremountainacademy.com. Thanks for watching! And I'll see you in the next video.