Answer:
Explanation:
Hello!
So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.
Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.
The hypotheses are:
H₀: The variables are independent.
H₁: The variables are not independent.
α: 0.05

r= total number of rows
c= total number of columns
i= 1, 2 (categories in rows)
j=1, 2, 3 (categories in columns)
To calculate the statistic you have to calculate the expected frequencies for each category:

Represents the marginal value of the i-row
Represents the marginal value of the j-column







Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:

Decision rule:
If
≥ 5.991, reject the null hypothesis.
If
< 5.991, do not reject the null hypothesis.
The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.
At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.
I hope this helps!