Question

A study conducted several years ago reported that 24 percent of public accountants changed companies within 4 years. The American Institute of CPAs would like to update the study. They would like to estimate the population proportion of public accountants who changed companies within 4 years with a margin of error of 4% and a 95% level of confidence. (Round your z value to 3 decimals. Round up your answers to the next whole number.)

a. To update this study, the files of how many public accountants should be studied?

b. How many public accountants should be contacted if no previous estimates of the population proportion are available?

Answer 1

Solution,

Given that,

a) = 0.24

1 - = 1 - 0.24 = 0.76

margin of error = E = 0.04

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.04)2 * 0.24 * 0.76

= 437.94

sample size = n = 438

b) =  1 - =   0.5

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

= (1.96 / 0.04)2 * 0.5 * 0.5

= 600.25

sample size = n = 601