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.)
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(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.

Answer 1

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:

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	0.11700526

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.