Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to perform hypothesis testing on standard deviations of drive through service times. Here's our problem statement: The accompanying data are drive through service times (in seconds) recorded at a fast food restaurant during dinner time. Assuming that dinner service times at the restaurant's competitor have a standard deviation of 53.5 seconds, use a 0.025 significance level to test the claim that service times at the restaurant have the same variation as service times at its competitor's restaurant. Use the accompany data to identify the null hypothesis, alternative hypothesis, test statistic, and P-value. Then state a conclusion about the null hypothesis.
OK, this first part of the problem wants us to identify the null and alternative hypotheses. The null hypothesis is by definition a statement of equality. So we know that the right answer is not going to be Answer option A or Answer option B, because in these instances, the null hypothesis is not a statement of total equality. So it's gotta be Answer option C or D.
How do we choose between them? We'll look at the alternative hypotheses. The alternative hypothesis is generally a statement that reflects the claim, unless the claim has any semblance of equality to it, in which case we take the complement. What's the claim here? Well, look back in the problem statement. Here's your key words right here --- we're "testing the claim that" --- and then what follows is the actual claim here, service times at the restaurant have the same variation as service times at the competitor's restaurant. So we're going to say that they're equal.
Well, equality by definition belongs to the null hypothesis. So therefore we have to take the complement and say that it's not going to be equal to, and that's going to be Answer option C. Nice work!
Now we're asked to compute the test statistic. And to do this, we have to actually run the hypothesis test. So we're going to click on this icon here to take a look at our data and then click on this icon to open up our data in StatCrunch. OK, we've got our data here in StatCrunch. I'm going to resize this so we can see more what's going on. And we don't need this window any more.
OK, so here in StatCrunch, we're going to run a hypothesis test by going to Stat --> Variance Stats (because we're looking at standard deviation and variance is the only option given here in StatCrunch when we're dealing with standard deviation) --> One Sample (because we've got just the one sample) --> With Data (because we have actual data here in the options window). I'm going to select the column where my data is located, and then I've got to make this area here for Hypothesis Test match the hypothesis test we got in the previous part.
But notice we're dealing here with variance. That means we've got to square everything that goes in the options window. So notice here in our original hypothesis we're using sigma as our population parameter, but here in StatCrunch in the options window, we've got sigma squared. So we've got to square everything that comes out. So 53.5 squared is what I want to put there in the options window for my claimed value. And now that I've done that, I can go ahead and hit Compute!, and out comes the chi squared test statistic, which is what we got here, chi squared. I'm asked to round to two decimal places. Excellent!
The next part of the problem asks for the P-value, which we get by looking here at the last value here in the table. I'm asked to round to three decimal places. Good job!
Now the last part asks us to state a conclusion about the null hypothesis. Well, our P-value (16.1%) is definitely greater than the 2.5% significance level we're asked to use for comparison. So therefore we're outside the reason of rejection, and there is not sufficient evidence. Whenever you fail to reject, there's not sufficient evidence. And we're doing this because the null hypothesis is not rejected; we fail to reject. Excellent!
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Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.