Question

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.
To test the claim, the following data is collected:

Day         | Mon     Tue     Wed     Thur    Fri

Absences | 37        15        12        23     43

Use this data to test the manager's claim at the 0.05 level of significance;

include all necessary steps for hypothesis testing.

Answer 1

We will do a Chi-square test for this.

H₀: Absences occur on the different week days with the same frequencies.

H₁: Absences do not occur on the different week days with the same frequencies.

Contingency table
Day	Mon	Tue	Wed	Thur	Fri	Total
Original (Oi)	37	15	12	23	43	130
Expected (Ei)	26	26	26	26	26	130
(Oi-Ei)2	121	121	196	9	289	736

Now, the degree of freedom is

The test statistics is given by

Then, the test statistics is

As the chi-square test is always a right tailed test, the critical value of for 0.05 level of significance is 9.49.

As the test statistics is greater than the critical value at 0.05 level of significance, we have sufficient evidence to reject H₀.

We do not have sufficient evidence to conclude that  absences occur on the different week days with the same frequencies.