Question

In order to set rates, an insurance company is trying to estimate the mean number of sick days that full time workers at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.1 days.

A. How large a sample must be selected if the company wants to be 90% confident that the true mean differs from the sample mean by no more than 1 day? No need to show work for the critical value.

B. Repeat part (A) using a 95% confidence interval. Which level of confidence requires a larger sample size? Explain. No need to show work for the critical value.

Answer 1

(A)

Sample Size (n) is given by:

Given:

= 0.10

From Table, critical values of Z = 1.645

= 2.1

e = 1

Substituting, we get:

So,

Answer is:

12

(B)

Sample Size (n) is given by:

Given:

= 0.05

From Table, critical values of Z = 1.96

= 2.1

e = 1

Substituting, we get:

So,

Answer is:

17

95% level of confidence requires a larger sample size