William R. Dillon. Thomas J. Madden, and Neil H. Firtle discuss a research proposal in which a telephone company wants to determine whether the appeal of a new security system varies between homeowners and renters. Independent samples of 140 homeowners and 60 renters are randomly selected. Each respondent views a TV pilot in which a test ad for the new security system is embedded twice. Afterward1 each respondent is interviewed to find out whether he or she would purchase the security system.
Results show that 25 out of the 140 homeowners definitely would buy the security system, while 9 out of the 60 renters definitely would buy the system.
a. Letting p1 be the proportion of homeowners who would buy the security system, and letting p2 be the proportion of renters who would buy the security system, set up the null and alternative hypotheses needed to determine whether the proportion of homeowners who would buy the security system differs from the proportion of renters who would buy the security system.
b. Find the test statistic z and the p-value for testing the hypotheses of part a. Use the p-value to test the hypotheses with a equal to .101 .051 .011 and .001. How much evidence is there that the proportions of homeowners and renters differ?
c. Calculate a 95 percent confidence interval for the difference between the proportions of homeowners and renters who would buy the security system. On the basis of this interval1 can we be 95 percent confident that these proportions differ? Explain.
An Excel add-in (MegaStat) output of the hypothesis test and confidence interval in parts b and c is given in Appendix 10.2.