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 standard deviations of alcohol treatments. Here's our problem statement: Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for treatment group of 21 people who drank ethanol and another group of 21 people given a placebo. The errors for the treatment group have a standard deviation of 2.20, and the errors for the placebo group have a standard deviation of 0.78. Use a 5% significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group. Assume that the two populations are normally distributed.
OK, the first part of this problem asks us to determine the null and alternative hypothesis. The null hypothesis is by definition a statement of equality, so here it looks like we’re not going to select answer option C. Of the options that remain, we need to look at the claim and compare it with the alternative hypothesis. The claim that we see in the problem statement is that the treatment group has errors that vary significantly more than the errors of the placebo group. Since the treatment group is mentioned first, we’re going to assume that that's going to have the subscript of 1 in the designations and the placebo group will have the subscript of two in its designations. So 1 should be greater than 2. And we see that's not answer option A. It’s not answer option B. It is answer option D. Good job!
Now the next part of the problem asks us to identify the test statistic. To do this, I’m going to load up StatCrunch. We don't have any data to put inside StatCrunch, but we are going to use the functionality of StatCrunch to get our test statistic. To do that, I'm going to go to Stat –> Variance Stats –> Two Sample (because I’ve got two samples I’m comparing) –> With Summary (because I don't have any actual data).
Again, the treatment group was mentioned first, so we’re going to assume this is the Sample 1. Notice we don't have the variance that's being asked for here in the options window, but we do have standard deviation, and we can get variance by squaring the standard deviation. So I pull out my calculator here, and I’m going to take that standard deviation for the first group, and I’m going to square it. That gives me the variance. And the sample size is 21. And then for the placebo group we see its standard deviation was 0.78, and I square it to get its variance. And it also has a sample size of 21.
The hypothesis test — notice how it’s written a little differently than what we see here in our answer options from the previous part of the problem. We can get the same thing, though, if we just take each of these expressions and divide by sigma sub 2 squared. And so we’re going to leave this one alone. But we need to change this inequality sign to “greater than” to match our alternative hypothesis. And then I just hit Compute! And here in my results window the second to last number is always the test statistic. So I’m going to put that here in my answer field. I’m asked to round to two decimal places. Excellent!
The next part asks me to identify the P-value, which we can also get from our results table. It's always the last number listed in the results table. Here we see it's listed as “< 0.0001" — this means that the actual value of the P-value is not zero but a number that's so small it is for all practical purposes zero. And so that's what I’m going to put here in my answer field. Good job!
And now the last part of the problem asks us to make a conclusion about the hypothesis test. Well, with a P-value of zero, we’re going to be less than whatever significance level we’re going to use for our test. Here we’re having a 5% significance level, so zero is definitely less than 5% which means were inside the region of rejection, and therefore we’re going to reject the null hypothesis. Whenever you reject the null hypothesis, you always “have sufficient evidence.” Nice work!
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Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.