Chapter 14.4, Problem 20E

Refer to Exercise 14.10. Test the hypothesis, at the 5% significance level, that the type A defects occur independently of the type B defects.

14.10.    Two types of defects, A and B, are frequently seen in the output of a manufacturing process. Each item can be classified into one of the four classes: A ∩ B, $A\cap \bar{B}$, $\bar{A}\cap B$, and $\bar{A}\cap \bar{B}$, where $\bar{A}$ denotes the absence of the type A defect. For 100 inspected items, the following frequencies were observed:

$A\cap B:48,A\cap \bar{B}:18,\bar{A}\cap B:21,\bar{A}\cap \bar{B}:13.$

Is there sufficient evidence to indicate that the four categories, in the order listed, do not occur in the ratio 5:2:2:1? (Use α = .05.)