Test the following hypotheses for a multinomial probability distribution by using the χ² goodness of fit test.\( H_0: \, p_A = 0.40, \, p_B = 0.20, \, \text{and} \, p_C = 0.40 \)\( H_a: \) The probabilities are not \( p_A = 0.40, \, p_B = 0.20, \, \text{and} \, p_C = 0.40 \)A sample of size 200 yielded 40 in category A, 120 in category B, and 40 in category C.Use \( \alpha = 0.01 \) and test to see whether the probabilities are as stated in \( H_0 \).a. Use the *p-value approach*. Use Table 3 of Appendix B.\[ \chi^2 = \_\_\_ \] (to 2 decimals)The *p-value* is [Select your answer]Conclusion:[Select your answer]b. Repeat the test using the *critical value approach*.\[ \chi^2_{0.01} = \_\_\_ \] (to 3 decimals)\[ \chi^2 = \_\_\_ \] (to 2 decimals)Conclusion:[Select your answer]

a. The sample of size 200 yielded. The expected values are, Category Yield(Observed) Proportion Expected A 40 0.40 200×0.40=80 B 120 0.20 200×0.20=40 C 40 0.40 200×0.40=80 The test statistic is, χ2=∑iObserved-Expected2Expected=40-80280+120-40240+40-80280=20+160+20=200 Thus, the test statistic is 200. The degrees of freedom is, df=k-1=3-1=2 The degrees of freedom is 2. Computation of P-value: The p-value of χ2-distribution at 2 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(200,2)”. The p-value is 0.000. Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.00) is less than the level of significance (0.01). Based on decision rule, reject the null hypothesis. Thus, Reject the null hypothesis.b. Critical value: The chi-square critical value of 0.01 level of significance at 2 degrees of freedom can be obtained using the excel formula “=CHISQ.INV.RT(0.01,2)”. The critical value is 9.210. The chi-square test statistic is 200. Decision rule: If test statistic > critical value, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The test statistic (200) is greater than the critical value (9.210). Based on decision rule, reject the null hypothesis.

Math

Statistics

Test the following hypotheses for a multinomial probability distribution by using the x goodness of fit test. Ho : PA = 0.40 , pB = 0.20, and pc = 0.40 Ha : The probabilities are not PA = 0.40 , pB = 0.20 , and pc = 0.40 A sample of size 200 yielded 40 in category A, 120 in category B, and 40 in category C. Use α = 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: (to 2 decimals) The p-value is Select your answer Conclusion: - Select your answer - b. Repeat the test using the critical value approach. (to 3 decimals) x² = (to 2 decimals) Conclusion: - Select your answer -

Test the following hypotheses for a multinomial probability distribution by using the x goodness of fit test. Ho : PA = 0.40 , pB = 0.20, and pc = 0.40 Ha : The probabilities are not PA = 0.40 , pB = 0.20 , and pc = 0.40 A sample of size 200 yielded 40 in category A, 120 in category B, and 40 in category C. Use α = 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: (to 2 decimals) The p-value is Select your answer Conclusion: - Select your answer - b. Repeat the test using the critical value approach. (to 3 decimals) x² = (to 2 decimals) Conclusion: - Select your answer -

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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