The following ANOVA table, based on information obtained for three samples selec

Question

The following ANOVA table, based on information obtained for three samples selected from three independent populations that are normally distributed with equal variances, has a few missing values. a) Find the missing values and complete the ANOVA table. Round to four decimal places. b) Using alpha = 01, what is your conclusion for the test with the null hypothesis that three populations are all equal against the alternative hypothesis that the means of the three population are not all equal? i. Reject H_0. Conclude that the means of the three populations are equal. ii. Reject H_0. Conclude that the means of the three populations are not equal. iii. Do not reject H_0. Conclude that the means of the three populations are equal. iv. Do not reject H_0. Conclude that the means are of the three populations are not equal.

Explanation / Answer

Question a)

Source of Variation

Degrees of Freedom

Sum of Squares

Mean Square

Value of the Test Statistics

Between

2

2 * 19.2813 = 38.5626

19.2813

Within

12 - 2 = 10

89.3677

89.3677 / 10 = 8.93677

19.2813 / 8.93677 = 2.158

Total

12

Source of Variation

Degrees of Freedom

Sum of Squares

Mean Square

Value of the Test Statistics

Between

2

38.5626

19.2813

Within

10

89.3677

8.93677

2.158

Total

12

Question b)

Null Hypothesis: All the population means are equal.

Alternative Hypothesis: At least one of the population mean differs.

The critical value for 2,10 degrees of freedom at 1% level of significance is given by 7.559

The test statistics is less than the critical value (2.158<7.559)

We fail to reject the null hypothesis.

Option iii) Do not eject Ho. Conclude that the means of the three populations are equal.

Source of Variation

Degrees of Freedom

Sum of Squares

Mean Square

Value of the Test Statistics

Between

2

2 * 19.2813 = 38.5626

19.2813

Within

12 - 2 = 10

89.3677

89.3677 / 10 = 8.93677

19.2813 / 8.93677 = 2.158

Total

12

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