First identify if the samples here are dependent paired or i

First identify if the samples here are dependent (paired) or independent. Then properly state the null and alternative hypotheses for the following situations:

1. Test the hypothesis that employees with a high school diploma have lower mean annual income than employees with a bachelor’s degree.

2. A health program measured the weights of a sample of women before and after a one month long exercise program. Test that the mean of the differences between before and after weights is different from zero.

Solution

1)

dependent paired samples

Ho : mean employees with a high school diploma >= mean annual income than employees with a bachelor’s degree.

H1 : mean employees with a high school diploma < mean annual income than employees with a bachelor’s degree.

2)

independent samples

Ho : mean before = mean after

H1 : mean before not equal mean after