Question

A company has just switched to a 4-day work week. The CEO measured the number of units produced by 8 employees one week before and one week after the change. The CEO would like to know if there is a difference in the number of units produced.

ID	Before	After
A	25	23
B	26	24
C	27	26
D	22	23
E	29	30
F	26	24
G	29	26
H	30	32

*Note: ID is used to keep each participant’s before and after number of units linked.

Using an alpha of .05, non-directional, conduct a hypothesis test to determine if there is a difference in the number of units produced between before and after the work week after the schedule change

Hypotheses in statistical form:

Test statistic:

Decision:

Effect size (if needed):

Write a results section. Remember to include all of the appropriate pieces, including your statistic in journal form and descriptive statistics.

Answer 1

From the sample data, it is found that the corresponding sample means are:

Also, the provided sample standard deviations are:

and the sample size is n = 8. For the score differences we have

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a two-tailed test, for which a t-test tor two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is alpha = 0.05, and the degrees of freedom are df = 7.

Hence, it is found that the critical value tor this two-tailed test is t_c = 2.365, for alpha = 0.05 and df = 7.

The rejection region for this two-tailed test is R = {t : |t|>2.365}