In the bookEssentials of Marketing Research,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. Afterward, 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. Lettingp₁be the population proportion of homeowners who would buy the security system, and lettingp₂be the population 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 statisticzand thep-value for testing the hypotheses of parta. (=0.05)

c. Determine the rejection rule:

d. What is the meaning of p-value for the hypothesis test in part a if= 0.1786-0.15= 0.0286?(Hint: p-value is the probability that we will get the sample values (or more extreme) from a population where the null hypothesis holds. THIS IS A TWO-SIDED TEST.)

e.We have(Click to select)very strongsomestrongextremely strongno

evidence that the proportions of homeowners and renters differ.

f.Calculate a 90percent confidence interval for the difference between the proportions of homeowners and renters who would buy the security system.

g.Can we conclude at the 90% confidence that the difference between the proportions of homeowners and renters who would buy the security system is greater than 0?

h.Can we conclude at the 90% confidence that the difference between the proportions of homeowners and renters who would buy the security system is less than 0.1?

In the book Essentials of Marketing Research. William R. Dillon, Thomas J. Madden. and Neil H. Fire 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. Aftemrard, each respondent is interviewed to nd out whether he or she would purchase the security system. Results show that 25 out of the 140 homeowners denitely would buy the security system. while 9 out of the 60 renters denitely would buy the system. a. Letting p1 be the population proportion of homeowners who would buy the security system. and letting p2 be le population proportion of renters who would buy le security system. set up the null and alternative hypotheses needed to determine wheler the proportion of homeowners who would buy the security system diers from the proportion of renters who would buy le security system. HEM92 = .0 Hazr'lpz a: .0 b. Find the test statistic z and the pvalue for testing le hypotheses of palt a. (u=0.05) Z: I , pvalue= c. Determine the rejection rule: Critical Value Rafe: Reject Ho if [Click to select} d. What is the meaning of p-value for le hypothesis test in part a if :91 732 = D.17860.15= 0.0286? (Hint: p~value is the probability that we will get the sample values (or more extreme) from a population where the null hypolesis holds. THIS IS A TWO-SIDED TEST.) (Click to select) e. We have (Click to select} evidence that the proportions of homeowners and renters differ. f. Calculate a 90 percent condence interval for the difference between the proportions of homeowners and renters who would buy the security system. 551*H2S g. Can we conclude at the 90% condence that the difference between the proportions of homeowners and renters who would buy the security system is greater than 0? (Click to select) h. Can we conclude at the 90% condence that the difference between the proportions of homeowners and renters who would buy the security system is less lan 0.1? (Click to select)