Question

A manufacturing company produces part QVZY for the aerospace industry, and this part can be manufactured using 3 different production processes. The production supervisor collected data on the number of defective units for each process. In Process 1, there were 29 defective units in 240 items. Process 2 produced 12 defective units in 180 items, and Process 3 manufactured 9 defective units in 150 items. At a significance level of 0.05, a chi-square test of independence was performed to determine if the quality of the items produced appears to be independent of the production process. What are the degrees of freedom for the chi-square statistic?

Select one of the following options:

A. 570
B. 520
C. 50

Answer 1

The degrees of freedom for the chi-square test in this context would be 2, calculated by the formula (r - 1) * (c - 1), where there are 3 rows for each process and 2 columns for defective and non-defective units.

Step-by-step explanation:

The question is related to the degrees of freedom for a chi-square test of independence. To calculate the degrees of freedom for this test, we use the formula (r - 1) * (c - 1), where 'r' is the number of rows and 'c' is the number of columns in the contingency table. In this case, there are 3 different production processes, so there are 3 rows. For the columns, we are comparing the number of defective to non-defective units, so there are 2 columns. Therefore, the degrees of freedom (df) are calculated as (3 - 1) * (2 - 1) = 2 * 1 = 2. Out of the options provided, none directly match the correct answer, so if you must choose from them, none is correct and there may have been a mistake in the question itself.