Question

Independent random samples of managers' yearly salaries (in $1000s) randomly selected from governmental and private organizations provided the following information. At 95% confidence, test to determine if there is a significant difference between the average salaries of the managers in the two sectors.

	Government	Private
	80	75
s	9	10
n	28	31

​Provide full solution with formulas

Answer 1

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized difference in mean values on either side.

Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 28 + 31 - 2 = 57

Since t0 = 2.0104 > 2.0025 = t{0.025, 57}, we reject the null hypothesis H0 in favor of the alternative hypothesis H1  

We have enough evidence to claim that there is a significant difference between the average salaries of the managers in the two sectors.