Question

A. Determine the sample size required to estimate a population proportion to within 0.038 with 97.9% confidence, assuming that you have no knowledge of the approximate value of the sample proportion.

Sample Size =

B. Repeat part the previous problem, but now with the knowledge that the population proportion is approximately 0.29.

Sample Size =

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.038

At 97.9% confidence level the z is,

= 1 - 97.9%

= 1 - 0.979 = 0.021

/2 = 0.0105

Z_/2 = 0.0105=2.31

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

= (2.31 / 0.038)² * 0.5 * 0.5

=924

Sample size = 924

Solution :

Given that,

= 0.29

1 - = 1 - 0.29 = 0.71

margin of error = E = 0.038

At 97.9% confidence level the z is,

= 1 - 97.9%

= 1 - 0.979 = 0.021

/2 = 0.0105

Z_/2 = 0.0105=2.31

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

= (2.31 / 0.038)² * 0.29 * 0.71

=761

Sample size = 761