Question

A. Determine the sample size required to estimate a population proportion to within 0.034 with 93.2% 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 0.3.

Answer 1

Solution:

Given that,

A ) = 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.034

At 93.2% confidence level the z is ,

= 1 - 93.2% = 1 - 0.932 = 0.068

/ 2 = 0.068 / 2 = 0.034

Z_/2 = Z_0.034 = 1.825

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

= (1.825 / 0.034)² * 0.5 * 0.5

= 720.38

n = sample size = 720

B ) = 0.3

1 - = 1 - 0.3 = 0.7

margin of error = E = 0.034

At 93.2% confidence level the z is ,

= 1 - 93.2% = 1 - 0.932 = 0.068

/ 2 = 0.068 / 2 = 0.034

Z_/2 = Z_0.034 = 1.825

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

= (1.825 / 0.034)² * 0.3 * 0.7

= 605.08

n = sample size = 605