Check my work Suppose the U.S. president wants to estimate the proportion of the

Question

Check my work 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 0.03 of the true proportion. Assume a 98% level of confidence. The president's political advisors found a similar survey from two years ago that reported that 54% of people supported health care revisions. (Use z Distrilbution Table-) 12 5 points a. How large of a sample is required? (Round up your answer to the next whole number.) eBook Hint 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) K Prex 4 of 8 Next 5:33 PM

Explanation / Answer

a) p=54% =0.54

q=1-p =1-0.54 =0.46

E=0.03

Z/2 for 98% confidence is 2.326

Margin of error, E = Z/2 × [(p×q)/n]

                              0.03 =2.326 x(0.54*0.46)/n

                              0.03 =2.326*0.498/n

                              0.03 =1.159/n

                              n =1.159/0.03

                              n =38.64

                              n=(38.64)^2

                              n=1494

b) when no estimate is given,then p=0.5

and q=1-p =1-0.5 =0.5

so

               E = Z/2 × [(p×q)/n]

                              0.03 =2.326 x(0.5*0.5)/n

                              0.03 =2.326*0.5/n

                              0.03 =1.163/n

                              n =1.163/0.03

                              n =38.7666

                              n=(38.7666)^2

                              n=1503

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