Investigation 9: Which Tire? (due Tues, Feb 14)

You may work with one other person on this assignment, handing in one report with both names.  Word-processed reports are preferred to hand-written ones. Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

Reconsider the “which tire” situation and the data that we collected in class.  When results from both sections are combined, 15 students chose the left front tire, 40 chose right front, 15 chose left rear, and 14 chose right rear. Consider our class to be a random sample of Cal Poly students.

a) Conduct a chi-square test of the hypothesis that students are equally likely to choose among the four tires. State the relevant hypotheses, determine the expected counts, show the calculation of the test statistic by hand, and report the P-value (as accurately as possible). Also summarize your conclusion.

Now consider the data as binary (dichotomous), depending on whether the student chose the “right front” tire or not.

b) Test whether the sample data provide compelling evidence that more than one-fourth of all Cal Poly students would choose the right front tire. Report the hypotheses, test statistic, and P-value. Summarize your conclusion.

Now suppose that you take a different random sample of Cal Poly students and find that 30% of the sample answers with the right front tire.

c) What additional information do you need to determine whether this sample proportion is large enough to provide strong evidence that more than 25% of all Cal Poly students would answer that way?

d) Conduct the appropriate test (based on a sample proportion of .3 answering “right front”) with a sample size of 100 and with a sample size of 500. Report the test statistic and P-value in each case.

e) Comment on how the strength of evidence against the hypothesis that 25% of the population would pick right front changes as the sample size increases, even as the sample proportion remains constant with 30% choosing right front. Also explain why this makes intuitive sense.