Question

If you polled 3,915 American adults and 1,751 of them felt worried about the future of the country, could you claim that less than the majority of American adults feel this way?

A) Construct a 95% confidence interval to support your conclusion.

B) If you were a campaign manager and wanted to conduct a poll with 99% confidence and a margin of error no more than 2.7%, how many people would you need to interview? Assume nothing is known about P^ or Q^

Answer 1

SOLUTION-

SAMPLE SIZE(N) = 3915

SUCCESS(X) = 1751

.SAMPLE PROPORTION() = 1751/3915 = 0.4472

A.) 95% CONFIDENCE INTERVAL IS GIVEN AS,

CRITICAL VALUE = 2.576

SO, THE 95% CONFIDENCE INTERVAL IS,

=

B.) FOR 99% CONFIDENCE INTERVAL, Z-MULTIPLIER = 2.576

ERROR(E) = 2.576 *S.E

WE WANT E<= 0.027

WE ALSO KNOW,

HENCE, 0.027 >= 2.576*S.E

OR,

OR,

SO,

HENCE THE MINIMAL SAMPLE SIZE NEEDED WILL BE 2276

****IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.