Exercise 13-5 Algo An analysis of variance experiment produced a portion of the accompanying ANOVA table. Assume normality in the underlying populations. Click here for the Excel Data File a. Fill in the missing statistics in the ANOVA table. Note: Round "MS" to 4 decimal places and "F" to 3 decimal places. ANOVA Source of Variation SS df MS F p-value Between Groups 12.45 3 0.0140 Within Groups 83.58 76 Total 96.03 79 b. Specify the competing hypotheses in order to determine whether some differences exist between the population means. $H_0: \mu_A = \mu_B = \mu_C = \mu_D$; $H_a$: Not all population means are equal. $H_0: \mu_A = \mu_B = \mu_C = \mu_D$; $H_a$: Not all population means are equal. $H_0: \mu_A = \mu_B = \mu_C = \mu_D$; $H_a$: Not all population means are equal. c. At the 10% significance level, what is the conclusion to the hypothesis test? Reject $H_0$: we can conclude that some means differ. Do not reject $H_0$: we cannot conclude that some means differ Do not reject $H_0$: we can conclude that some means differ. Reject $H_0$: we cannot conclude that some means differ.
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MS(Between Groups) = SS(Between Groups) / df(Between Groups) = 12.45 / 3 = 4.15 MS(Within Groups) = SS(Within Groups) / df(Within Groups) = 83.58 / 76 = 1.10 Show more…
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An analysis of variance experiment produced a portion of the accompanying ANOVA table. Assume normality in the underlying populations. (You may find it useful to reference the F table.) a. Specify the competing hypotheses in order to determine whether some differences exist between the population means. b. Fill in the missing statistics in the ANOVA table. (Round "MS" to 4 decimal places and "F" to 3 decimal places.) c. At the 5% significance level, what is the conclusion of the test?
Madhur L.
14. Consider the following ANOVA table, the null hypothesis for this ANOVA problem is Source of Variation SS DF MS F Between ? 3 ? 3 Within ? ? 20 Total ? 18 (A) H0: μ1 = μ2 (B) H0: μ1 = μ2 = μ3 (C) H0: μ1 = μ2 = μ3 = μ4 (D) None of the above. 15. Refer to above problem, The total sum of squares (SSTO) is (A) 80. (B) 180. (C) 300 (D) 480 16. Refer to above problem, The variance between samples is (A) 20. (B) 60 (C) 180 (D) 300 (E) 480 17. Refer to above problem, the value of the test statistics is (A) 15 (B) 12 (C) 4 (D) 3 18. Refer to above problem, at α = 0.05, the critical value is (A) 3.06 (B) 3.29 (C) 4.15 (D) 8.70 (E) 以上皆非 19. Refer to above problem, the p-value is (A) greater than 0.10 (B) between 0.05 to 0.10 (C) less than 0.05 (D) None of the above 20. Refer to above problem, at α = 0.1, we conclude that A. Reject H0, there is enough evidence to conclude that there is a difference in the population mean. B. Reject H0, there is not significant difference between the four population means. C. Fail to reject H0, there is not significant difference between the four population means. D. None of the above.
Qudsiya A.
Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. 1) What can you conclude about the equality of the population means? Source DF SS MS F p Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80 A) Accept the null hypothesis since the p-value is greater than the significance level. B) Accept the null hypothesis since the p-value is less than the significance level. C) Reject the null hypothesis since the p-value is greater than the significance level. D) Reject the null hypothesis since the p-value is less than the significance level. 2) Consider the partially completed one-way ANOVA summary table. Source Sum of Squares Degrees of Freedom Mean Sum of Squares F Between 270 Within 18 Total 810 21 The total number of observations for this ANOVA procedure is A) 20. B) 18. C) 21. D) 22. 3) Consider the partially completed one-way ANOVA summary table. Source Sum of Squares Degrees of Freedom Mean Sum of Squares F Between 270 Within 18 Total 810 21 The mean square within for this ANOVA procedure is A) 90. B) 72. C) 46. D) 30.
T. L.
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