Question

A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the 0.01 significance level.

	Pension Plan
Job Class	Plan A	Plan B	Plan C
Supervisor	43	43	43
Clerical	46	46	37
Labor	66	39	33

State the decision rule. Use 0.01 significance level. (Round your answer to 3 decimal places.)

H₀: Pension plan preference and job class are not related.

H₁: Pension plan preference and job class are related.

Compute the value of chi-square. (Round your answer to 3 decimal places.)

What is your decision regarding H₀?

Answer 1

First we compute the expected value of reach of the 9 cells here as:
Ei = (Sum of column)*(Sum of row)/ Grand Total

Then, the chi square test statistic contritbuion for each cell here is computed as:

The circular brackets in the above table contain the expected frequencies, while the square bracket contain the chi square test statistic contribution values. Therefore the chi square test statistic here is computed as:

Df = (num of columns - 1)*(num of rows - 1) = 4

The p-value now is computed here as: ( from the chi square distribution tables)

As the p-value here is 0.114612 > 0.01 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore there is insufficient evidence of association between the two variables here.