Test the following hypotheses by using the x goodness of fit test. Ho: PA H: The population proportions are not pa = 0.40, PB = 0.40, and pc 0.40, PB = 0.40, and Pc 0.20 = 0.20. A sample of size 200...

Extracted text: Test the following hypotheses by using the x goodness of fit test. Ho: PA H: The population proportions are not pa = 0.40, PB = 0.40, and pc 0.40, PB = 0.40, and Pc 0.20 = 0.20. A sample of size 200 yielded 80 in category A, 20 in category B, and 100 in category C. Use a = 0.01 and test to see whether the proportions are as stated in Ho. (a) Use the p-value approach. Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion. Do not reject Ho. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. Reject Ho. We conclude that the proportions differ from 0.40, 0.40, and 0.20. Reject Ho. We conclude that the proportions are equal to 0.40, 0.40, and 0.20. Do not reject Ho. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. (b) Repeat the test using the critical value approach. Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.) test statistic < test="" statistic=""> State your conclusion. Do not reject Ho. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. Do not reject Ho. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. Reject Ho. We conclude that the proportions are equal to 0.40, 0.40, and 0.20. Reject Ho. We conclude that the proportions differ from 0.40, 0.40, and 0.20. O O O O