Question

An analysis of variance experiment produced a portion of the accompanying ANOVA table. (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.

• H₀: μ_A = μ_B = μ_C = μ_D; H_A: Not all population means are equal.

• H₀: μ_A ≥ μ_B ≥ μ_C ≥ μ_D; H_A: Not all population means are equal.

• H₀: μ_A ≤ μ_B ≤ μ_C ≤ μ_D; H_A: Not all population means are equal.

b. Fill in the missing statistics in the ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "MS" to 4 decimal places and "F" to 3 decimal places.)

c. At the 5% significance level, what is the conclusion to the test?

• Reject H₀; we can conclude that some means differ.

• Do not reject H₀; we cannot conclude that some means differ.

• Do not reject H₀; we can conclude that some means differ.

• Reject H₀; we cannot conclude that some means differ.

Answer 1

Answer Date: 15/04/2019 To test the hypothesis is that there are some differences exist between the population means at 5% level of significance. a) The null and alternativehypothesis is, Ha : at least one is unequal. b) The mean square between groups is, BG dfsG 18.26 6.0867

The mean square error is, SSE 83.67 68 = 1.2304 The F-test statistics is, MS BG obtMSE 6.0867 1.2304 4.947 The F-test statistics is 4.947. c) The F-critical value is,

From the F distribution at 5% level of significance table, show degree of freedom treatment 3 and degree of freedom error 68 as result the F-critical value is 2.740. The F-critical value is 2.740. Decision The F-test statistics is 4.947 is greater than F-critical value which is 2.740, the null hypothesis is rejected at 5% level of significance. There is sufficient evidence that here are some differences exist between the population means. The result is statistically significant