Question

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 99% level of confidence. The president’s political advisors found a similar survey from two years ago that reported that 62% of people supported health care revisions.  (Answers must be whole numbers.)

1. How large of a sample is required?

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

Answer 1

Solution :

Given that,

= 0.62

1 - = 1 - 0.62 = 0.38

margin of error = E = 0.03

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.03)2 * 0.62 * 0.38

=1737.09

Sample size = 1738

(B)

Solution :

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.03

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.03)2 * 0.5 * 0.5

=1843.27

Sample size = 1844