est the following hypotheses for a multinomial probability distribution by using the x oodness of fit test. Họ : PA = 0.40 , PB = 0.40, and pc = 0.20 Ha : The probabilities are not PA = 0.40 , pB = 0.40 , and Pc = 0.20 sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C. Ise a = 0.01 and test to see whether the probabilities are as stated in Ho - . Use the p-value approach. Use Table 3 of Appendix B. 2 = 122.5 (to 2 decimals) he p-value is less than 0.005 onclusion: Conclude the proportions differ from 0.4, 0.4, and 0.2. . Repeat the test using the critical value approach. (to 3 decimals) -0.01 9.21 (to 2 decimals)

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Test the following hypotheses for a multinomial probability distribution by using the x
goodness of fit test.
Ho : PA = 0.40 , PB = 0.40, and pc = 0.20
Ha : The probabilities are not
PA = 0.40 , pB = 0.40 , and Pc = 0.20
A sample of size 200 yielded 60 in category A, 120 in category B, and 20 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 =
122.5
(to 2 decimals)
The p-value is less than 0.005
Conclusion:
Conclude the proportions differ from 0.4, 0.4, and 0.2.
b. Repeat the test using the critical value approach.
(to 3 decimals)
=
9.21
(to 2 decimals)
Transcribed Image Text:Test the following hypotheses for a multinomial probability distribution by using the x goodness of fit test. Ho : PA = 0.40 , PB = 0.40, and pc = 0.20 Ha : The probabilities are not PA = 0.40 , pB = 0.40 , and Pc = 0.20 A sample of size 200 yielded 60 in category A, 120 in category B, and 20 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 = 122.5 (to 2 decimals) The p-value is less than 0.005 Conclusion: Conclude the proportions differ from 0.4, 0.4, and 0.2. b. Repeat the test using the critical value approach. (to 3 decimals) = 9.21 (to 2 decimals)
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