In the book Essentials of Marketing Research, WilliamR. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a researchproposal in which a telephone company wants to determine whetherthe appeal of a new security system varies between homeowners andrenters. Independent samples of 140 homeowners and 60 renters arerandomly selected. Each respondent views a TV pilot in which a testad for the new security system is embedded twice. Afterward, eachrespondent is interviewed to find out whether he or she wouldpurchase the security system.

Results show that 25 out of the 140 homeowners definitely would buythe security system, while 9 out of the 60 renters definitely wouldbuy the system.

(a) Letting p₁ be theproportion of homeowners who would buy the security system, andletting p₂ be the proportion of renters whowould buy the security system, set up the null and alternativehypotheses needed to determine whether the proportion of homeownerswho would buy the security system differs from the proportion ofrenters who would buy the security system.

	H0: p1 – p2 versus Ha: p1 – p2

(b) Find the test statistic z and thep-value for testing the hypotheses of part a. Usethe p-value to test the hypotheses with α equalto .10, .05, .01, and .001. How much evidence is there that theproportions of homeowners and renters differ? (Round theintermediate calculations to 3 decimal places. Round your z valueto 2 decimal and p -value to 3 decimalplaces.)

z=

p-value=

	Reject H0 at α =   , but not at α =  Â

(c) Calculate a 95 percent confidence intervalfor the difference between the proportions of homeowners andrenters who would buy the security system. On the basis of thisinterval, can we be 95 percent confident that these proportionsdiffer? (Round your answers to confidence interval to 4decimal places. Negative amounts should beindicated by a minus sign. )

Confidence interval = [    ,