Chapter 8.2, Problem 41E

To determine

Explain the conclusion to the test based on the given values.

Answer to Problem 41E

There is sufficient evidence to conclude that not all the population means are significantly equal for Groups A, B, and C.

Explanation of Solution

The null and alternative hypotheses can be written as follows:

Null hypothesis:

$H_0$: There is no significant difference between the population means of Groups A, B, and C.

Alternative hypothesis:

$H_a$: Not all the population means are significantly equal of Groups A, B, and C.

From the computer output, the p-value for the test is 0.002.

Decision rule:

If the p-value is less than or equal to the level of significance, reject the null hypothesis. Otherwise, do not reject the null hypothesis.

Conclusion:

Here, the p-value is 0.002.

Therefore, the p-value is less than any common levels of significance, such as 0.10, 0.05, and 0.01.

Hence, reject the null hypothesis.

Therefore, there is sufficient evidence to conclude that not all the population means are significantly equal for Groups A, B, and C.