Mathway | Algebra Problem Similarities and Differences Mathway Statistics Proble
ID: 2907986 • Letter: M
Question
Mathway | Algebra Problem Similarities and Differences Mathway Statistics ProblerCh 9 Quiz Xstuder https://newconnect.mheducation.com/flow/connect.html Seved Suppose the U.S president wants to estimate the proportion of the population that supports his current policy toward revisions in the health care system. The president wants the estimate to be within 0.05 of the true proportion. Assume a 95% level of confidence. The president's political advisors found a similar survey from two years ago that reported that 64% of people supported health care revisions. (Use z Distribution Table) a. How large of a sample is required? (Round up your answer to the next whole number.) b. How large of a sample would be necessary If no estimate were available for the proportion supporting current policy? (Round up your answer to the next whole number.)Explanation / Answer
a. We have ,
Zalpha/2 * ( p * ( 1-p) / n )0.5 < 0.05
Z = Z0.05/2 = Z0.025 = 1.96
p = 0.64
1.96 * ( 0.64 * ( 1- 0.64 ) / n )0.5 < 0.05
n0.5 > 18.816
n = 354
Sample size of 354 is required.
b. We assume that p =0.5 ( since we are not given anything about proportion estimate)
Zalpha/2 * ( p * ( 1-p) / n )0.5 < 0.05
1.96 * ( 0.50 * ( 1- 0.50 ) / n )0.5 < 0.05
n0.5 > 19.6
n = 385
Sample size of 385 would be necessary if no estimate were available for the proportion.