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!

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.

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.

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!

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.

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!

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.

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.

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.

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.

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.

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.

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.

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to use bootstrap methods to construct a proportion confidence interval estimate.  Here's our problem statement: In a study of the accuracy of fast food drive through orders, a restaurant had 38 orders that were not accurate among 451 orders observed.  Use the bootstrap method to construct a 90% confidence interval estimate of the proportion of orders that are not accurate.  Use the 200 accompanying bootstrap samples.  How does the result compare to the 90% confidence interval 0.063 to 0.106 constructed using the sample proportion?

OK, the first part of this problem asks for a confidence interval estimate. And to construct that, we're going to take the bootstrap samples that they give us and use percentiles to construct the confidence interval.  To do that, we need to take our data.  And normally we put it into StatCrunch, but since we're doing percentiles I find it easier to do that in Excel. I'm going to put the data in Excel, which I've already done here.  And now we can see here in Excel, here's our data.

So for finding percentiles, the first thing we need to do is sort our data.  Here in Excel, we can do that by going up to Data and then in the Data ribbon we select Sort.  And now we want to sort by that second column "Not Accurate."  And we want to order it from smallest to largest.  So I press OK.  Now my data has been reordered.

We need to take these numbers here, which are counts of orders that are not accurate, and we need to convert them into proportions because we're building a confidence interval estimate on proportions, not counts.  So to transform each of these numbers, we're going to let Excel do the calculation for us.  And to do that, I'm going to put my --- I'm going to select the cell right next to that first sample row.  And I'm going to type in the formula that I want Excel to calculate.  So I start out by pressing equals, and then I'm going to use my left arrow key to select that cell just to the right, and then we're going to divide by the total number of observations from the orders (which we see here in the problem statement is 451).  I press Enter, and there Excel has calculated everything for me.

Now notice here it says we want to round our values to three decimal places.  And I can do that in Excel automatically.  I just come here, and I'm going to go back to Home, and then here in my Number area, I'm going to use this arrow right here to decrease the decimal to three decimal places.  And lo and behold, Excel has got everything rounded for me, and this is great!  All I gotta do is just read the numbers when we're all said and done.

OK, now to copy this formula down, I can do it in either one of two ways.  I can either drag it down --- notice when I take the cursor over that right bottom corner of my cell, it changes into this smaller cross.  When it's at that smaller cross, I can hold down the left button on my mouse, and then I can drag the formula down, and it'll copy everything for me.  Now there's 200 of these that I need, so I'm going to be dragging for awhile.  It's not the most efficient way to do this.

The more efficient way to do this would be to select this column here --- I mean, excuse me, this cell --- and then I'm going to hit Ctrl + C to copy it.  And then I'm going to go over one to the left.  And then to get down to the very bottom, I'm going to press Ctrl + Down Arrow, and notice it instantly brought me down to the bottom of that row.  I'm going to go back one because I want my values there in Column C.  And now I'm going to press Ctrl + Shift + Up Arrow.  So now I've not only moved my cursor up to the top of the column there, but now I've also selected everything in between, and that's where I want these values to appear.  Now I have to just paste it in.  And I do that by pressing Ctrl + V.  E viola!  There's everything copied in.

So now we've got everything that we need to calculate our percentiles.  But in order for our count to not be off so much, we're going to delete this first row that we see here.  So the first thing I'm going to do is select it by clicking on the left mouse here.  And then while my cursor is still in that same position, I'm going to right click on my mouse, and I hit Delete.  And now that first row has been deleted.

So now we can use percentiles to get our confidence interval estimate.  Our confidence level is 90%.  That means 90% of these values are going to be inside our confidence interval, which means the remaining 10% is out.  Half of that 10% is going to be on the left, and half is going to be on the right.  So 5% is going to be here on the left outside of the confidence interval.  And what does that translate to as far as how many rows do we need to count down?  Well, 5% of the 200 rows that we have --- if I get my calculator out, I got 5% of the 200 rows gives me 10.  So I need to go down to Row 10.  Here's Row 10.  And because we're using percentiles, we want the number in the next row.  So here in Row 11, the number I need his 0.06.  That's my lower limit for my bootstrap confidence interval.

To get the upper limit, we're going to do the same thing but going from the bottom up.  So here we went from --- here we went to 10.  And now we're going to go back into Excel, and I'm going to go down to the bottom of my list.  And I want to go to Row 190 --- 90 is 10 less than 200.  And the number I need is in the next row down, which is 0.111.  Nice work!

And now the second portion of this problem asks, "If some portion of the confidence intervals overlap, the confidence intervals are not significantly different. The results of the two intervals are" --- then there's a blank.  So if you click on the drop down, then you we can see that they either are or are not significantly different.  Well, that's defined here as whether or not they overlap.  So if we look here up here at the top to see if they overlap or not, look at their intervals here.  Notice what we have here.  We've got here in this interval, we've got 0.063 is our lower limit.  Here we got 0.06.  And then the upper limit here we've got 0.106, and here we've got 0.111.  So there's quite a bit of overlap between these two confidence intervals.  And that means they're not significantly different.

Now the second part here says the interval from the bootstrap method is --- and we have to look at our interval and compare it with the actual interval that we have there.  So here we've got 0.063, 0.060.  So this is going to be on the left side of this interval.  And then 0.111 is going to be to the right of our upper limit here (0.106).  So this confidence interval that we constructed with bootstrapping is wider than the other that we were given there on the problem statement.  I check my answer.  Good job!

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 find and interpret summary statistics of celebrity earnings.  Here's our problem statement: Find the mean, median, mode, and midrange for the data, and then answer the given questions.  Listed below are the highest amounts of net worth in millions of dollars of all celebrities.  What do the results tell us about the population of all celebrities based on the nature of the amounts?  What can be inferred about their precision?

OK, Part A asks us to find the mean.  And to do this, we're going to take our data and dump it into StatCrunch.  I dumped my data here into StatCrunch.  And now I'm going to resize this window so we can see a little better everything that's going on here.  OK, now in StatCrunch, to get my summary stats, I'm gonna go to Stat --> Summary Stats --> Columns (because my data set is listed in a column here).  In the options window, I'm going to select the column where my data is located.  And then down here under Statistics, notice that we've got multiple statistics that are selected by default.  All we really need for this first part of the problem is to select the mean.  So I'm just going to select mean and get that out.

Now at this point I can go ahead and hit Compute!, and StatCrunch will give me the mean value that I need to put in my answer field here in my assignment.  However, I'm going to be a little smart and look ahead and notice that I'm going to have to do this same procedure to calculate the median, the mode, and the midrange.  So since I'm here already, let's just calculate everything at once, and then we don't have to go back and forth through the menu options multiple times.  So I'm going to calculate multiple statistics all at once.

So we already have the mean value listed.  That's the first one we need to calculate.  The next one is the median.  As I scroll down here, I find the median, and then I hold the Control key down while I select the median.  And now I've got both the mean and the median selected. I do the same thing for the remaining statistics.  The next one is the mode, so I'm going to scroll down here to the bottom, because that's where the mode is, hold the Control key and click on the mode.

And then the midrange --- if you go up and down here through the list, you'll notice there is no midrange.  So that means we need to actually calculate it ourselves.  But to do that we're going to actually select numbers from this list of statistics to help us do that.  There's three ways to calculate the midrange based on the numbers that they give us here, but you only need to select two of them.  So the three from what you need to select two are the range, the min and the max.  You only need to select two of them. I'm actually going to select all three because when we get to that part of the problem, I'll show you the three different ways to calculate this.  And then you can decide which way is going to work best for you.

Notice we have the selections that we've made here are in a certain order.  This is the order in which we selected them.  This is also the order in which they're going to appear in the results window.  So I purposefully selected these statistics in this order because that's the order in which we're going to have to put them in our answer field, and this just makes it easier to go back and forth between the assignment and the results window to put the numbers in so we don't get confused.  Once I hit Compute!, I get my results window, and here are all the statistics that I need to calculate with the mean up front.  So I'm just gonna put that here in my assignment.  Nice work!

Now, Part B asks for the median.  We already have that calculated here, so all I have to do is just take the number out and stick it in the answer field.  Excellent!

And Part C asks for the mode.  And it's the same story here, so I'm just going to put that number in here.  Nice work!

Part D asks for the midrange.  StatCrunch does not calculate the midrange directly.  It's a simple enough calculation.  I don't know why they didn't program it in, but they didn't.  So now we've got to go old school.  And I'll pull up my calculator here, and there's three ways to calculate it.  The way I prefer to calculate it is to take half the range and then add it to the min.  So I'm going to take half the range, which means I divide by two, and then I'm going to add that to the minimum value.  I get 197.5.  This is the mid range.

Now notice I get the same number if I take half the range, which again means dividing by two, and I'm going to subtract this number from the maximum value.  Argh!  I pressed the wrong button on my calculator.  OK, let's try this.  I take half the range, and I'm going to subtract that from the maximum value.  Here we go.  Notice we get the same number out.  I can get the same number out a third way by taking the minimum value and the maximum value and averaging those values together.  So I take 155, add it to 240, and then I take half of that sum.  Notice I get the same number out.  So there's no one right way to do it.  There's multiple paths to the same answer, and that's why I say you need to pick the way that's right for you and then just be consistent with it.  So every time you're asked to find the midrange, you just use the same calculation procedure, and you can just go through and get the answer that you need.  I'm going to put that here in my answer field.  Excellent!

And now the first question in Part E asks, "What do the results tell us about the population of all celebrities?"  We've got four answer options here.  So let's take a look at each one of them in turn.  Answer option A says, "Apart from the fact that all other celebrities have amounts of net worth lower than those given, nothing meaningful can be known about the population."  Well, to assess this statement, we need to go back and look at our data set and ask, "What is the data telling us? Where did the data come from?"  The data here are listing the highest amounts of net worth of all celebrities.  So this is a small proportion of all celebrities.  It's not the whole population; it's the people that are at the very top of the list.  These are the people who make the most money.  So most people in the population are going to be making less than this.  And so we can't really get much information about the population since this is just a very small sampling of a select portion of the population.

So it looks like Answer option A makes sense, but before we go ahead and submit this for our answer, let's check the other answer options to make sure we've got the right answer.  Answer option B says, "Apart from the fact that all other celebrities have amounts of net worth lower than those given, the results in Parts A, B and D do not give meaningful results."  OK, that makes sense, because as we just said, we're looking at a small sample of the population that's not representative of the population.  However, “the result from Part C shows that the most common celebrity net worth is equal to the mode”?  Well, that's not true because most of the celebrities are going to be earning far less than the numbers given here in our data set.  So we can't actually say that this is true.  Therefore we're not going to select Answer option B.

Answer option C says, "The results tell us that all celebrities are expected to have amounts of net worth approximately equal to one of the measures of center found in Parts A through D."  Again, that doesn't make any sense because the data that we have here is for a small select portion of the population that's not representative of the population.  So we're not going to select Answer option C.  Answer option D says, "The results tell us that the most common celebrity net worth is the mode, but all other celebrities are expected to have net worths approximately equal to the mean, median, or midrange."  Again, this is nonsense because this sample does not represent the whole population.  It's only the highest numbers from the list of the net worths of all the celebrities.  So again, we're not going to select Answer option D.  It looks like Answer option A is the one we want.  Excellent!

And now the last question here in both Part E and the problem asks, "Based on the nature of the amounts, what can be inferred about the precision?"  Well, again, let's look at these values here --- or these answer options, rather --- and see how they fare out.  So Answer option A says, "Since no information is given, nothing can be said about the precision of the given values."  Well, let's look up here at our data set.  We look at the individual data values, and do you notice a pattern?  As you look at each one of these, you should notice that most of these are ending in 5.  There's a couple of them here that end in 0.

So it looks like we have a set number for the last digit in the data set.  It's either going to be a zero or a five, and that suggests that these numbers have been rounded to the nearest $5 million amount.  So "since no information is given, nothing can be said about the precision of the given values"?  No, I wouldn't say that's true.  We can actually look here and say that, yes, something's going on with this data set.  So we could --- we actually probably could say something about the precision.  It looks like there's some rounding going on.  So let's not select Answer option A.

Answer option B says, "The values are all whole numbers, so they appear to be accurate to the nearest whole number."  Well, that's not really true because if we were accurate to the nearest whole number, why is it that the only last digit that we see is either a zero or a five?  Why don't we see any other numbers?  And you would think that you would see other numbers in the data set, but we only see zeros or fives.  So it's probably not rounded to the nearest whole number.  It's rounded to the nearest $5 million value.

Answer option C says, "Since celebrity information is public, these values can be assumed to be unrounded."  Well, what is the public status?  If it's public or private, what does that have to do with whether or not the numbers are rounded or not?  Nothing.  There's nothing that ties those two together.  And so Answer option C is just absolute nonsense.

Now we get Answer option D says that the values end all in zero and five as they appear to be rounded estimates.  This is exactly right.  This is what we've observed by evaluating all the other answer options.  This appears to be the correct one, so we're going to select it. 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 as I 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 conduct mean hypothesis testing on back pain treatment data.  Here's our problem statement: Researchers conducted a study to determine whether magnets are effective in treating back pain.  The results are shown in the table for the treatment with magnets group and the sham or placebo group.  The results are a measure of reduction in back pain.  Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.  Complete Parts A and B below.  Use a 0.05 significance level for both parts.

OK, we can see here that the data that we need to run our hypothesis test is here in this table.  And notice that the treatment group is Group 1 and the placebo group is Group 2.  This corresponds with the usual practice that you see here in the problem statement where the one that's mentioned first is Group 1 and the one that's mentioned second is Group 2.  So here we have the first part to Part A, which says, "Test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.  What are the null and alternative hypotheses?"  Well, here you can see that the treatment group was Group 1.  The sham or placebo group is Group 2.  So we're testing the claim that Group 1 has a greater mean than Group 2.

What's the null alternative hypothesis that we want?  Well, the null hypothesis is always a statement of equality.  So looking at my answer options here, I don't want Answer options B or D because those null hypotheses are not statements of equality.  How do we choose between Answer options A and C?  Well, we look at the alternative hypothesis.  Remember we're testing the claim that Group 1 has a greater mean than Group 2.  And look at my alternative hypothesis here.  That's reflected here in Answer option C.  Well done!

Now the second part of Part A asks for the test statistic.  Notice it's a t score.  So when I go into StatCrunch to get my hypothesis testing, I know I need to look for a t score.  Let's resize this windows so we can see better what's going on here.  And now to get my hypothesis test, we go to Stat --> T Stats (because we want a t score) --> Two Sample (because we have two samples we're comparing) --> With Summary (because we don't have any actual data).

Here in my options window, it asks me for the summary stats.  And these are the same numbers that come out of the table that we see here in the problem statement.  So I'm going to go ahead and type in those numbers.  The sample mean is x-bar, so here we have the sample mean for the first group.  Sample standard deviation is s.  And the sample size is n.  Let me go ahead and enter in those same numbers for the second sample.  And then down here, notice the default selection on the radio button here is for hypothesis testing, so we'll leave that alone.  Notice that the area here needs to match what we have here, but it's organized differently in StatCrunch than it is in your assignment.  So if we know here, from what we've actually selected as the right answer, that our null hypothesis says that mu1 equals mu2.  Here we've got mu1 minus mu2.  Well, if mu1 and mu2 are the same number and we subtract them, we're going to get zero.  So we're going to leave this claimed value alone.  Then here in this field, we need to make sure our inequality sign matches what we have here.  And now we've got everything we need.  So we hit Compute!, and our test statistic [is the] second to last value there in the results window table.  I'm asked to round to two decimal places.  Fantastic!

Now the next part asks for the P value.  That's the last value listed here in the results window table, right next door to the test statistic.  I'm asked to round to three decimal places.  Excellent!

Now the next part for Part A says, "State the conclusion for the test."  To do this, let's compare the P value with our significance level.  Here our P value is almost 42% [with a] significance level of 5%.  So our P value is way larger than our significance level, which means we're outside the region of rejection.  And whenever you're outside the region of rejection, you're going to fail to reject.  And every time you fail to reject, there is not sufficient evidence.  Good job!

And now the last part of Part A asks, "Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?"  Well, if we have a larger sample size, it's going to be easier for the test to detect a statistically significant difference.  Remember, there's a difference between practical significance and statistical significance.  And what we're testing with the hypothesis test is statistical significance.  With a larger sample size, you might actually get, you know, more --- I guess a more sensitivity to detecting that statistical significant difference.  Let's look at our drop downs here to see what we could select from that.

Here we're at the first one.  We're asked to select between the mean and the standard deviation.  We're going to choose the mean because that's what our hypothesis test is testing.  It's testing a difference in the population means.  So we want to be looking at the sample means for comparison.  The second drop down asks us to compare the sample means for each of the two different groups.  So we look at here, x-bars, our sample mean, and we see that the treatment group has a greater mean than the placebo group.  And then finally, we just got done saying that it is valid to argue that magnets might appear to be effective, because with the larger sample size you're more likely to detect the statistical significant difference and that's what you need in order for the test to come out to say that, yeah, the magnets are going to be effective.  Good job!

And now Part B of this problem asks us to construct a confidence interval.  Well, that's very easily done.  If we go back here to our results window in StatCrunch, I can click on Options --> Edit.  That takes me back to my options window.  I scroll down here, switch that radio button from hypothesis test to confidence interval, I need to make sure I put in the right level here --- we've got a 5% significance level, but remember we've got two samples now with a one tailed test, so that means I need to take out two alpha, not just one.  So that 95% now becomes 90%.  And here are my lower and upper limits for my confidence interval.  I'm asked to round to three decimal places, so I will do that here.  There's my lower limit.  And now here is my upper limit.  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 find the sample size needed to estimate a mean student completion rate confidence interval.  Here's our problem statement: In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full time college students who earn a bachelor's degree in four years or less.  Find the sample size needed to estimate that percentage.  Use a 0.05 margin of error, and use a confidence level of 95%.  Complete Parts A through C below.

Part A says, "Assume that nothing is known about the percentage to be estimated."  Well, to solve this problem there is a sample size estimator inside StatCrunch.  So let's pull up StatCrunch.  I don't think it'll be of much use to us because --- I'll show you in a moment.  It actually requires us to know the standard deviation of our sample size, and there's nothing about standard deviation there in our problem statement.  So that option there in StatCrunch isn't all that useful to us.  But I'll show you here.  We can move this around, resize that so we can see a little bit better what's going on.  And there we go.

So if I go to T Stats --> One Sample --> Width/Sample Size, you can see here.  Standard deviation is required to actually make the estimate for the sample size.  Well, we don't know anything in here about standard deviation.  There's nothing in here that indicates that, and there's nothing that we can use to estimate standard deviation.  So this option is not going to be very useful for us.  This means we have to go old school.  So here's our equation for estimating sample size.  We need a z score, which we then square, multiply by p-hat, which is the percentage that we want to be successful, and q-hat is the compliment of p hat.  And then we divide all that by the margin of error squared.

First up, let's go get our z score, which means I need to go back into StatCrunch and pull up my Normal calculator.  Remember that z scores come from the standard Normal distribution, which has a mean value of zero and a standard deviation of one.  So here I've got the default values, and that's exactly what I need for my standard Normal distribution.  I'm going to select the Between option here because we want a z score coming from two tails here.  And the reason why I know that is because if I go back and look at my equation, I've got z alpha over two.  That means only half of the alpha is in the right tail of my distribution.  So there must be another half in the left tail of the distribution.  I've got alpha split between two tails.  So I want to use that Between option there.

In StatCrunch, this option gives us the percentage of the total area that is between the boundaries here, between the tails.  So that in this case, that's going to be equal to the confidence level that we want.  So I'm going to come down here and replace this with my 95% confidence level.  And now when I hit Compute!, the z scores that come out, which is the boundary on these tails.  This is the z score that I need.  So I'm going to pull out my calculator.  I'm going to put 1.96 squared (because the 1.96 is coming from that z score here; it's on the right tail of my distribution).  So I've got the 1.96 squared.  Now the rest of the formula says I need p-hat, q-hat.  Well, we don't know anything about the percentage of what's successful.  And so in that case we're going to estimate p-hat q-hat with 0.25.  So I multiply this by 0.25, and then I'm going to divide by the square of my margin of error, which here in the problem statement is 0.05, so divide it by 0.05 squared.  And now I get three 384.16.  I'm instructed here to round up to the nearest integer.  So that's going to give me 385.  Nice work!

Now Part B says, "Assume prior studies have shown that about 55% of full time students earned bachelor degrees in four years or less."  Now we have a value for p-hat q-hat.  So if you want, go ahead and run through the same calculation that we just ran through for Part A using this same formula.  You can start from the very beginning if you want, or you could follow the shortcut that I'm going to show you here.  I know that the new p-hat is 55%.  So I'm gonna take this value that's still in my calculator, and I'm going to multiply it by 0.55 (55%), and then I'm going to multiply that by q-hat.  And to do that, I'm going to take the compliment of p-hat.  So I can either do that in my head and get the 45% that I know it is, or I can let the calculator do that for me and say one minus 0.55.  It's going to give you the 0.45.  And now I'm going to divide this by the old p-hat q-hat, which was the 0.25, and there's my new value.  Round up to the nearest integer.  E voila!  Well done!

Now Part C says, "Does the added knowledge in Part B have much of an effect on the sample size?"  Well, we went from 385 down to 381.  So our sample size got reduced by, like, four people.  That's not a very large reduction; it's only slightly reduced.  So I would say it doesn't have that much of an effect.  And I'm going to select the answer option here that basically says that --- "No, it only slightly reduces the sample size."  Well done!

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.