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 p_{1} be the
proportion of homeowners who would buy the security system, and
letting p_{2} 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.
H_{0}: p_{1} – p_{2} (Click to select) 0 0.05 greater than 0 less than 0 versus H_{a}: p_{1} – p_{2} (Click to select) 0 greater than 0 less than 0 does not equal to 0 (b) Find the test statistic z and the
pvalue for testing the hypotheses of part a. Use
the pvalue 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.)

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