Question

In order to set rates, an insurance company is trying to estimate the 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 2.8 days. How large a sample must be selected if the company wants to be 95% confident that the true mean differs from the sample mean by no more than 1 day?

Answer 1

Answer: 31

Step-by-step explanation:

Formula to find the sample size is given by :_

$n=(\dfrac{z^*\cdot \sigma}{E})^2$

, where z*= critical value corresponds to confidence level.

$\sigma$ = population standard deviation.

E= Margin of error.

As per given , we have

$\sigma=2.8$

E=1

We know that critical value corresponding to 95% confidence level = z*=1.96

Then, the required sample size would be :

$n=(\dfrac{(1.96)\cdot (2.8)}{1})^2$

$n=(5.488)^2$

$n=30.118144\approx31$

Hence, the required minimum sample size = 31