In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madde
ID: 3254686 • Letter: I
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) State null hypothesis and alternative hypothesis. H_o: H_a: b) Find the sample proportion of homeowners who would buy the security system, the sample proportion of renters who would buy the security system, and the grand proportion. Sample Proportion of Homeowners: Sample Proportion for Renter: Grand Proportion: c) It is given that the test statistic is 0.4926;use this information to find the p-value using the appropriate table. Draw the curve and highlight the corresponding area d) At the .05 significance level, do you reject or retain the null hypothesis? How about at the .01 significance level. Circle the correct answer and explain using the p-value found in part c). At alpha = .05 Reject H_o/Retain H_o Why? At alpha = .01 Reject H_o/Retain H_o Why? e) Find a 95% confidence interval for the difference between the two proportions of homeowners and renters who would buy the security system. Interpret the result.Explanation / Answer
a. H0: Proportion of homeowners who would buy the system = Proportion of renters who would buy the system
Ha: Proportion of homeowners who would buy the system not equal to Proportion of renters who would buy the system
b. Sample proportion of homeowners = 25/140 = 0.178
Sample proportion of renters = 9/60 = 0.15
Grand proportion = (25+9)/(140+60) = 34/200 = 0.17
c. The test statistic is z(standard normal distribution) = 0.4926
From standard normal table, we get, p value = 2(1-0.689) = 2*0.311 = 0.622
d. Based on p value, we reject the null hypothesis both at the 0.05 and 0.01 level(As p value>0.05,0.01)
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