According to a national representative survey done by Consumer Reports , you sho

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 (30% compared with 25%). (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 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 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 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

Ans:

95% confidence interval for p1-p2

=(0.30-0.25)+/-1.96*sqrt((0.3*(1-0.3)/400)+(0.25*(1-0.25)/400))

=0.05+/-1.96*0.0315

=0.05+/-0.062

=(-0.012,0.112)

b)As,Confidence interval for p1-p2 includes 0,so we can say that there is no difference in both proportions.

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.

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