Chapter 12.3, Problem 19E

Test the following hypotheses by using the χ² goodness of fit test.

     $\begin{array}{l}{H}_0:p_{\text{A}}=.40,p_{\text{B}}=\mathrm{.40.}\text{ and}{p}_{\text{C}}=.20\\ H_{\text{a}}:\text{ The}\text{population}\text{proportions are not}\\ p_{\text{A}}=.40,p_{\text{B}}=.40,\text{ and}{p}_{\text{C}}=.20\end{array}$

A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C. Use α = .01 and test to see whether the proportions are as stated in H₀.

1. a. Use the p-value approach.
2. b. Repeat the test using the critical value approach.