Question

Employees from Company A and Company B both receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.05 level of significance? Write out the hypothesis and explain the testing procedure.

Answer 1

Explanation:

This is a test of the mean difference between 2 independent groups or populations.

Let μ1 be the mean annual bonus of Company A's employees and μ2 be the mean annual bonus of Company B's employees.

The random variable is μ1 - μ2 = difference in the mean annual bonus of Company A's employees and the mean annual bonus of Company B's employees

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 ≤ μ2 H0 : μ1 - μ2 ≤ 100

The alternative hypothesis is

H1 : μ1 > μ2 H1 : μ1 - μ2 > 100

This is a right tailed test because of the inequality sign at the alternative hypothesis. We need to take samples of annual bonuses from both company's employees and find the averages. Then we would determine the test statistic as well as the p value. We would use the p value with the level of significance to make decisions