Question

The Human Resources manager of Slam’s Club was shocked by the revelations of gender discrimination by WalMart and wants to check whether there is a gender difference in average salaries in his firm. He takes a random sample of 145 male employees and 75 female employees. The average salary for the males is 54.372 thousands of USD, female average salary is 49.773 thousands of USD. He assumes that the variability of the salaries is equal and finds the pooled standard deviation of 10.844 thousands USD. What are the approximate values of the test statistics and critical value for the appropriate hypothesis test (significance level = 5%)? Answer is: test statistic = 2.982, and critical value = 1.971. I can get the test statistic. The part I need help on is how to get the critical value. please show the excel command used to obtain it in detail.

Answer 1

Solution:

Given:

n₁ = 145

n₂ = 75

Level of significance = 5% = 0.05

Since we assume  that the variability of the salaries is equal , that is population variances are equal, then

degrees of freedom are given by:

df = n₁ + n₂ - 2

df = 145 + 75 - 2

df = 218

Since we have to test whether there is a gender difference in average salaries in his firm, we use two tailed test.

Thus:

Two tail area = Level of significance = 5% = 0.05

We use following Excel command:

=T.INV.2T(probability , df )

=T.INV.2T(0.05,218)

2T means two tails.

thus t critical value = 1.970906 = 1.971

In Excel 2007, we use following command:

=TINV(probability,df)

=TINV(0.05,218)

which gave us same result.

=1.970906

=1.971

thus t critical value= 1.971