Question

The proportion of public accountants who have changed companies within the last three years is to be estimated within 5%. The 99% level of confidence is to be used. A study conducted several years ago revealed that the percent of public accountants changing companies within three years was 20. (Use z Distribution Table.) (Round the z-values to 2 decimal places. 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) = 0.20

1 - = 1 - 0.20 = 0.80

margin of error = E = 0.05

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.58

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

= (2.58 / 0.05 )² * 0.20 * 0.80

= 426.01

sample size = n = 427

b) =  1 - =   0.5

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

= (2.58 / 0.05)² * 0.5 * 0.5

= 665.64

sample size = n = 666