Question

In the book Essentials 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) 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.

H₀: p₁ – p₂   (Click to select)   0   0.05   greater than 0   less than 0   versus H_a: p₁ – p₂   (Click to select)   0   greater than 0   less than 0   does not equal to 0   

(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 α equal to .10, .05, .01, and .001. How much evidence is there that the proportions of homeowners and renters differ.(Round the intermediate calculations to 3 decimal places. Round your z value to 2 decimal and p -value to 3 decimal places.)

z =
p - value =

Reject H₀ at α =   (Click to select)   no values   0.1, 0.05, 0.01 and 0.001   0.1, 0.05, and 0.01   0.1   0.1 and 0.05  , but not at α =   (Click to select)   no values   0.1, 0.05, 0.01 and 0.001   0.1, 0.05, and 0.01   0.1 and 0.05   0.1  ;   (Click to select)   very strong   some   strong   no   extremely strong   evidence that p₁ and p₂ 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 interval, can we be 95 percent confident that these proportions differ? (Round your answer to confidence interval to 4 decimal places. Negative amount should be indicated by a minus sign. )

Answer 1