ANOVA The XLSTAT display below results from using the one-way analysis of variance test with the three samples.

a. What is the null hypothesis?

b. Assuming a 0.05 significance level, what conclusion is indicated by the displayed results?

The XLstats results are given for a one-way analysis test for three different samples.

a.

In an analysis of variance test, the mean of three or more populations is compared using their samples. The test compares the mean values using the comparison of variances.

The hypotheses for the ANOVA test is,

\({H_o}:\)(null) the mean of all three samples is equal.

\({H_a}:\)(alternative) at least one sample has a mean value different from others.

Thus, the null hypothesis assumes that all group means are equal.

b.

From the test result, the F-statistic is observed as 1.9104, and the p-value is 0.1729.

The significance level is 0.05.

The decision rule for the test:

• In case the p-value is less than 0.05, the null hypothesis is rejected. In this case, it can be concluded that there is insufficient evidence that the mean of all samples is equal.
• In case the p-value is greater than 0.05, the null hypothesis is failed to be rejected. In this case, it can be concluded that there is sufficient evidence that the mean of all samples is equal.

As per the decision rule, the p-value is greater than 0.05 (significance level). Thus, the null hypothesis is failed to be rejected.

As a result, it can be concluded that there is enough evidence to conclude that the mean of the three samples is equal.