Question

A study conducted several years ago reported that 19 percent of public accountants changed companies within 5 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 5 years with a margin of error of 5% and a 90% level of confidence. To update this study, the files of how many public accountants should be studied?
How many public accountants should be contacted if no previous estimates of the population proportion are available?

Answer 1

Answer: If p=0.19, then to update this study, the files of 98 public accountants should be studied.

If no prior estimate of the population proportion is given then to update this study, the files of 271 public accountants should be studied.

Step-by-step explanation:

As per given , we have

Margin of error : E = 0.05

Critical value for 90% confidence : $z_{\alpha/2}=1.645$

Prior estimate of population proportion: p= 0.19

Formula for sample size :

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.19(1-0.19)(\dfrac{1.645}{0.05})^2\\\\=166.582899\approx167$

∴ To update this study, the files of 167 public accountants should be studied.

If no prior estimate of the population proportion is given , then

we take p= 0.05

Required sample size :

$n=0.5(1-0.5)(\dfrac{1.645}{0.05})^2\\\\=270.6025\approx271$

∴ To update this study, the files of 271 public accountants should be studied.