Question

Assuming that s = 18,000 is a reasonable estimate for what sample size would be needed to ensure that we could estimate the true mean salary of all production managers with more than 15 years experience within $4200 if we wish to be 95% confident?

Answer 1

The minimum sample size required is 71.

Explanation:

The (1 - α)% confidence interval for population mean is:

`CI=\bar x\pm z_(\alpha/2)* (\sigma)/(√(n))`

The margin of error for this interval is:

`MOE=z_(\alpha/2)* (\sigma)/(√(n))`

It is provided that the population standard deviation σ can be estimated by the sample standard deviation s.

The given information is:

s = 18000,

Margin of error = $4200.

Confidence level = 95%

The z-value for 95% confidence level is,

`z_(\alpha/2)=z_(0.05/2)=z_(0.025)=1.96`

*Use a z-table for the critical value.

Compute the sample size required as follows:

`MOE=z_(\alpha/2)* (\sigma)/(√(n))`

`n=[(z_(\alpha/2)* \sigma )/(MOE)]^(2)`

`=[(18000* 1.96)/(4200)]^(2)`

`=70.56\\\approx71`

Thus, the minimum sample size required is 71.