14. One criterion used to evaluate employees in the assembly section of a large

Question

14. One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to fin out whether there is a relationship between years of experience and defect rate. A defect rate n terms of High, Average or Low is calculated for each worker in a yearly evaluation. The results tor 100 workers based on years of experiences are given in the table below. ule? Referring to the Table below, at alpha =0.05 level of significance, what would be the decision r 1 Year 16.919 O b. Reject Ho if chi-square > 15.507 O c. Reject Ho if chi-square > 11.143 O d. Reject Ho if chi-square > 9.488 tho arsemhly section of a large factory is the

Explanation / Answer

Solution:

Here, we have to write the decision rule for the given chi square test for two categorical variables.

First of all we have to find the critical value for this test.

Critical value is based on the level of significance or alpha value and degrees of freedom.

We are given level of significance or alpha value = 0.05

Now, we have to find degrees of freedom.

DF = (r – 1)*(c – 1)

Where, r = number of rows and c = number of columns

From the given table, we have r = 3, c = 3

So, DF = (3 – 1)*(3 – 1) = 2*2 = 4

Now, by using Chi square table with = 0.05 and DF = 4, we have to find critical value which is given as below:

Chi square Critical value = 9.487729

So, we reject the null hypothesis H0 if chi square > 9.488

So, correct answer is d.

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