Question

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

Answer 1

(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