Suppose the U.S. president wants an estimate of the proportion of the population

Question

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.04 of the true proportion. Assume a 99% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.57. (Use z Distribution Table.)

How large of a sample is required? (Round the z-values to 2 decimal places. Round up your answer to the next whole number.)

How large of a sample would be necessary if no estimate were available for the proportion supporting current policy? (Round the z-values to 2 decimal places. Round up your answer to the next whole number.)

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.04 of the true proportion. Assume a 99% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.57. (Use z Distribution Table.)

Explanation / Answer

1)Take (.57)(1-.57)= . 2451

Z score for 99% is 2.576

Required sample size is (t/b)^2 s^2 ,  where t is the critical value cutting off .005 in each tail
(here 2.576), b is the margin of error (here .04),
and s^2 is the variance in the pop. (here .57(1-.57)=.2451).

(2.576/.04)^2=4147.36

(.2451)(4147.36)=1016.5179. Round up to 1017voters.

2) Just use an estimate of .50 if they dont give you one. So take (.50)(1-.50)=.2500

Thus (4147.36)(.2500)= 1036.84.  Round up to 1037voters.

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