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

Question

#7 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 200 men and 200 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_______________  

Explanation / Answer

z/2 = 1.9599

Lower Bound = (p1 - p2) - z/2•p1(1 - p1)/n1+ p2(1 - p2)/n2 = -0.0447

Upper Bound = (p1 - p2) + z/2•p1(1 - p1)/n1+ p2(1 - p2)/n2 = 0.1447

Confidence Interval = (-0.04475974888020734, 0.14475974888020743)



Interpretation of a confidence interval:
Since we do not know if the confidence interval (-0.0447, 0.1447)
contains the difference in population proportions (p1 - p2) or not,
we are only 95% confident that (-0.0447, 0.1447) contains
the difference in proportions (p1 - p2).

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