Chapter 12.1, Problem 1E

Test the following hypotheses for a multinomial probability distribution by using the $X^2$ goodness of fit test.
$H_0:p_A=.40,p_B=.40,$ and $p_C=.20$
   $H_0:$ The probabilities are not
   $p_A=.40,p_B=.40,$ And
   $p_C=.20$
A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C. Use $\alpha =.01$ and test to see whether the probabilities are as stated in $H_0$ .
a. Use the p-value approach.
b. Repeat the test using the critical value approach.