According to a national representative survey done by Consumer Reports , you sho
ID: 3371912 • Letter: A
Question
According to a national representative survey done by Consumer Reports, you should always try to negotiate for a better deal when shopping or paying for services.† Tips include researching prices at other stores and on the Internet, timing your visit late in the month when salespeople are trying to meet quotas, and talking to a manager rather than a salesperson. Suppose that random samples of 400 men and 400 women are taken, and that the men were more likely than the women to say they "always or often" bargained (40% compared with 35%). (Use p1 and p2 for the proportions of men and women, respectively, who say they "always or often" negotiate for a better deal.)
(a) Construct a 95% confidence interval for the difference in the proportion of men and women who say they "always or often" negotiate for a better deal. (Round your answers to three decimal places.)
to
(b) Do the data indicate that there is a difference in the proportion of men and women who say they "always or often" negotiate for a better deal? Explain.
Since the value p1 ? p2 = 0 is not in the confidence interval, it is not possible that p1 ? p2 = 0. We should not conclude that there is a difference in the proportion of men versus women who say they "always or often" negotiate for a better deal.Since the value p1 ? p2 = 0 is in the confidence interval, it is possible that p1 ? p2 = 0. We should not conclude that there is a difference in the proportion of men versus women who say they "always or often" negotiate for a better deal. Since the value p1 ? p2 = 0 is not in the confidence interval, it is not possible that p1 ? p2 = 0. We should conclude that there is a difference in the proportion of men versus women who say they "always or often" negotiate for a better deal.Since the value p1 ? p2 = 0 is in the confidence interval, it is possible that p1 ? p2 = 0. We should conclude that there is a difference in the proportion of men versus women who say they "always or often" negotiate for a better deal.
Explanation / Answer
The statistical software output for this problem is:
Two sample proportion summary confidence interval:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
95% confidence interval results:
Hence,
a) 95% confidence interval will be:
(-0.017, 0.117)
b) Since the value p1 - p2 = 0 is in the confidence interval, it is possible that p1 ? p2 = 0. We should not conclude that there is a difference in the proportion of men versus women who say they "always or often" negotiate for a better deal.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 160 400 140 400 0.05 0.034186986 -0.017005261 0.11700526Related Questions
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