Question

we wish to estimate the mean salary of all 649 employees at a certain company. Assume it is known that the standard deviation of all employee salaries is $3780. A SRS of 49 employees shows a sample mean salary of $26,700 and a sample standard deviation of $3910

A)what is the population? _____ what is the variable of interest and is it quantitative or qualitative? _______

B)Find a 95% confidence interval for the mean salary of all 649 employees. ______

C)How many employees must be sampled in order to guarantee the margin of error is the 95% confidence interval does not exceed $525? _____

Answer 1

A)

All the 649 employees constitute the population.

The variable of interest is the estimate of mean salary of all employees which is a quantitative value.

B)

We know that the 95% confidence interval for population mean is given by:

C)

We know that the 95% confidence interval for population mean is given by:

So, Margin of error =

We want to find 'n' such that

So, n = 200, which is the number of employees that must be sampled in order to guarantee that the margin of error for the 95% confidence interval does not exceed $525.