In: Statistics and Probability
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.
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(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=
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(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 answers to confidence interval to 4 decimal places. Negative amounts should be indicated by a minus sign. )
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