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 0.03 of the true proportion. Assume a 98% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.54.

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

Answer 1

Given that,

(a)

= 054

1 - = 1 - 0.54 = 0.46

margin of error = E = 0.03

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.326 / 0.03)² * 0.54 * 0.46

= 1493.24 = 1493

Sample size = 1493

(b) Given that,

= 0.5 (when p hat is not given then use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.03= 0.03

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z_/2 = Z_0.01 = 2.326

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.326 * 0.03)² * 0.5 * 0.5

= 1502.85= 1503

Sample size = 1503

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