Question

.

A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be

90​%

confident that the sample mean is correct to within

plus or minus±​$40

of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately

​$487.

a. How large a sample is​ necessary?

b. If management wants to be correct to within

plus or minus±​$15​,

how many employees need to be​ selected?Click here to view page 1 of the cumulative standardized normal distribution table.

Click here to view page 2 of the cumulative standardized normal distribution table.

a. How large a sample is​ necessary?  

​(Round up to the nearest​ integer.)

If management wants to be correct to within plus or minus​$15​, how many employees need to be​ selected?   ​(Round up to the nearest​ integer.)

Answer 1

Sample size = ( Z * / E)² , Where E is margin of error.

a)

Sample size = ( 1.645 * 487 / 40)²

= 401.11

Sample size = 402 (Rounded up to nearest integer)

b)

Sample size = ( 1.645 * 487 / 15)²

= 2852.38

Sample size = 2853 (Rounded up to nearest integer)