A television network commissioned a telephone poll of randomly sampled men. Of the 703 respondents who had children, 23% said "yes" to the question "Are you a stay-at-home dad?" Answer parts a and b.
a) To help market commercial time, the network wants an accurate estimate of the true percentage of stay-at-home dads. Construct a
90% (20.4%, 25.6%).
b) An advertiser of baby-carrying slings for dads will buy commercial time if at least 27% of men are stay-at-home dads. Use your confidence interval to test an appropriate hypothesis, and make a recommendation to the advertiser.
A. Since the confidence interval extends below 27%, we are sure that over 27% of men are stay-at-home dads. The company should buy the ads.
B. Since the confidence interval does not extend below 27%, we are sure that over 27% of men are stay-at-home dads. The company should buy the ads.
C. Since the confidence interval does not extend below 27%, we can't be sure that over 27% of men are stay-at-home dads. The company should not buy the ads.
D. Since the confidence interval extends below 27%, we can't be sure that over 27% of men are stay-at-home dads. The company should not buy the ads
Please answer question B highlighted in bold. with explanation
(B) From part (A), we get 90% confidence interval = (20.4%, 25.6%).
We can see that the upper limit (25.6%) is lower than 27% , this shows that the percentage of man who are "stay-at-home dads" is significantly less than 27%.
So, We cannot make sure that the percentage is above 27%.
Therefore, correct answer is option D
D. Since the confidence interval extends below 27%, we can't be sure that over 27% of men are stay-at-home dads. The company should not buy the ads
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