Howdy! I’m Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we’re going to learn how to use StatCrunch to perform hypothesis testing on means of female pulse rates. Here’s our problem statement: Use the pulse rates and beats per minute of a random sample of adult females listed in the data set available below to test the claim that the mean is less than 77 bpm. Use a 0.01 significance level.
OK, the first part of our problem asks us to provide the null and alternative hypotheses. Remember, the null hypothesis by definition is a statement of equality, so obviously answer B is not going to be correct because this null hypothesis is not a statement of equality. Of the remaining answer options, we look for the alternative hypothesis, and typically alternative hypothesis is to match the claim. Here in the problem statement, the claim is that the mean pulse rate is less than 77 bpm, so were going to select the claim that represents the alternative hypothesis. That’s going to be our correct answer. So that's going to be this answer option here. Well done!
Now, the next part of our problem asks us to determine the test statistic. To do this, we’re going to take the data that they give us here and we’re going to dump it into StatCrunch. So here's my data in StatCrunch. And now I'm going to resize this window so we can see everything a little bit better.
OK, so now here in StatCrunch, I’m going to go up to Stat — and when you’re testing the mean, you could select Z Stats or T Stats. To know which one to select, we need to ask ourselves the key question, which is “Do we know what the population standard deviation is?” In this case, we don't know what it is; there’s nothing to indicate what it is in the problem statement. And that means we need to use the Student-t distribution.
So I’m going to select T Stats –> One Sample (because I’ve only got the one sample) –> With Data (because I have actual data in StatCrunch). Here in my options window, I'm going to select the column where my data is located. And then I'm going to make sure — here under Hypothesis Test I’m going to make sure this matches what we've listed over here in the previous part of the problem. That matches, then I hit Compute! and here comes the answers that I'm looking for. So the test statistic is going to be the second to last number here in this table in the results window. I’m asked to round to two decimal places. Fantastic!
Now the next part asks me to determine the P-value. The P-value is back here in the results window. It's always the last value listed in the results table. I’m asked to round to three decimal places. Excellent!
And now the last part of the problem asks me to state the final conclusion that addresses the original claim. To do this, I’m going to compare the P-value with the significance level. Here in the problem statement, we have a 1% significance level, but our P-value was almost 26%. That's definitely above 1%. Therefore, we are outside the region of rejection, and we’re going to fail to reject the null hypothesis. Because we fail to reject the null hypothesis, there is always insufficient or not sufficient evidence to support the claim. The claim was that the mean pulse rate is less than 77 bpm. I check my answer. 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.
Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.