In a survey of 1016 ?adults, a polling agency? asked, \"When you? retire, do you

Question

In a survey of 1016 ?adults, a polling agency? asked, "When you? retire, do you think you will have enough money to live comfortably or not. Of the 1016 ?surveyed, 535 stated that they were worried about having enough money to live comfortably in retirement. Construct a 99?% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.

A. There is a 99?% probability that the true proportion of worried adults is between ___ and ___.

B. 99?% of the population lies in the interval between ___ and ___.

C. There is 99?% confidence that the proportion of worried adults is between ___ and ___.

Explanation / Answer

Solution:- Given that n = 1016, x = 535

p = 535/1016 = 0.527

99% confidence interval for Z = 2.576

99% confidence interval for the proportion adults = p +/- Z*sqrt(pq/n)

= 0.527 +/- 2.576*sqrt(0.527*0.473/1016)

= 0.487, 0.567

=> option C.  There is 99?% confidence that the proportion of worried adults is between 0.487 and 0.567

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