Question

In: Statistics and Probability

Suppose the U.S. president wants an estimate of the proportion of the population who support his...

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 90% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.56. (Use z Distribution Table.)

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.)

  Sample   
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.)

  Sample   

Solutions

Expert Solution

Solution,

Given that,

a) = 0.56

1 - = 1 - 0.56 = 0.44

margin of error = E = 0.03

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

= (1.65 / 0.03 )2 * 0.56 * 0.44

= 745.36

sample size = n = 746

b) =  1 - =   0.5

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

= (1.65 / 0.03)2 * 0.5 * 0.5

= 756.25

sample size = n = 757


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