Question

Suppose the prime minister wants an estimate of the proportion of the population who support his current policy on health care. The prime minister wants the estimate to be within 0.03 of the true proportion. Assume a 80% level of confidence. The prime minister's political advisors estimated the proportion supporting the current policy to be 0.3. (Round the intermediate calculation to 2 decimal places. Round the final answer to the nearest whole number.)

a. How large of a sample is required?

b. How large of a sample would be necessary if no estimate were available for the proportion that support current policy?

Answer 1

Solution :

Given that,

= 0.3

1 - = 1 - 0.3 = 0.7

margin of error = E = 0.03

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 =0.10

Z/2 = Z0.10= 1.28 Using z table    )  

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

= (1.28 / 0.03)2 * 0.3 * 0.7

=382.29

Sample size = 383

(B)

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.03

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 =0.10

Z/2 = Z0.10= 1.28 Using z table    )  

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

= (1.28 / 0.03)2 * 0.5 * 0.5

=455.111

Sample size =456