Test the following hypotheses for a multinomial probability distribution by using the x² goodness of fit test. Ho: PA=0.40, PB = 0.20, and pc = 0.40 Ha The probabilities are not : A sample of size 200 yielded 50 in category A, 100 in category B, and 50 in category C. Use a = 0.01 and test to see whether the probabilities are as stated in Ho. a. Use the p-value approach. Use Table 3 of Appendix B. x² = 153.75 (to 2 decimals) The p-value is less than 0.005 Conclusion: Conclude the proportions differ from 0.4, 0.2, and 0.4. b. Repeat the test using the critical value approach. X0.01 (to 3 decimals) x² = (to 2 decimals) PA = 0.40, PB=0.20, and pc = 0.40 Conclusion: Conclude the proportions differ from 0.4, 0.2, and 0.4.