Question

The proportion of public accountants who have changed companies within the last three years is to be estimated within 4%. The 95% 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 22. (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,

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

(a)

= 22% = 0.22

1 - = 1 - 0.22 = 0.78

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

= (1.96 / 0.04)² * 0.22 * 0.78

= 412

sample size = 412

412 public accountants should be studied .

(b)

= 0.5

1 - = 1 - 0.5 = 0.5

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

= (1.96 / 0.04)² * 0.5 * 0.5

= 600.25 = 600

sample size = 600

600 public accountants should be contacted .