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 0.02 of the true proportion. Assume a 99% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.41. A. How large of a sample is required? B b. How large of a sample would be necessary if no estimate were available for the proportion supporting current policy? (Round intermediate values to 3 decimal points. Round your answer up to the next whole number.)

Answer 1

The sample size for part A is 4025, and the sample size for part B is 4160

What is the margin of error(MOE)?

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

$\rm MOE = Z\times \dfrac{s}{\sqrt{N}}$

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            N is the number of samples.

MOE = 0.02

99% level of confidence

a = 1 - 0.99 = 0.01

Z(a/2) = 2.58

The president's political advisors estimated the proportion supporting the current policy to be 0.41.

A) p = 0.41

$\rm N = p(1-p)(\dfrac{Z_{\alpha/2}}{MOE})^2$

$\rm N =0.41(1-0.41)(\dfrac{{2.58}}{0.02})^2$

N = 4025.45 ≈ 4025

B) How large of a sample would be necessary if no estimate were available for the proportion supporting the current policy

$\rm N =0.5(1-0.5)(\dfrac{{2.58}}{0.02})^2$

N = 4160

Thus, the sample size for part A is 4025, and the sample size for part B is 4160

Learn more about the Margin of error here:

brainly.com/question/13990500

#SPJ1