Salaries of 45 college graduates who took a statistics course in college have a mean, x overbar, of $ 61 comma 300. assuming a standard deviation, sigma, of $18 comma 246, construct a 99% confidence interval for estimating the population mean mu.

We are given:
sample size= n = 45
sample mean = x = 61,300
sample standard deviation =18,246

Since the population standard deviation is not known we will use t distribution to find the confidence interval.

Confidence interval = 99%
Degrees of freedom= n - 1 = 45 – 1 = 44
Critical t value = 2.692

The 99% confidence interval will be:

Thus, the 99% confidence interval for the population mean is:
53978 to 68622