5. According to a report, more and more young adults are drinking coffee daily. An independent study conducted using a random sample of 500 young adults produces a 95 percent confidence interval for p, the proportion of all young adults who drink coffee daily. The interval was reported to be (0.14, 0.18). Which of the following is correct?

(A) The margin of error for the given interval is 0.04.

(B) We can conclude that a majority of young adults drink coffee daily.

(C) There is a 95% probability that the true proportion of young adults that drink coffee is between 0.14 and 0.18.

(D) We can be 95% confident that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18.

(E) If this procedure were to be repeated many times, 95% of the resulting confidence intervals will display that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18.

Question

Advanced Placement (AP)

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22 January, 05:46

5. According to a report, more and more young adults are drinking coffee daily. An independent study conducted using a random sample of 500 young adults produces a 95 percent confidence interval for p, the proportion of all young adults who drink coffee daily. The interval was reported to be (0.14, 0.18). Which of the following is correct?

(A) The margin of error for the given interval is 0.04.

(B) We can conclude that a majority of young adults drink coffee daily.

(C) There is a 95% probability that the true proportion of young adults that drink coffee is between 0.14 and 0.18.

(D) We can be 95% confident that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18.

(E) If this procedure were to be repeated many times, 95% of the resulting confidence intervals will display that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18.

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Answers (1)

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Nick Tyler · Answer 1

D

Explanation:

The correct answer is (D). Note that the margin of interval is 0.02 (half the length of the interval). The interval is not entirely above 0.5, so we cannot conclude that a majority of young adults drink coffee daily. The interval gives no information about what is happening over time. Finally, if we were to repeat the procedure many times, the resulting intervals would capture the true population proportion 95% of the time rather than strive to adhere to the results of this one random sample.