Question

Consider the partially completed one-way ANOVA summary table below. In conducting the test whether all the population means are equal, all of the below assumptions must hold except the populations follow.

Answer 1

The assumptions for a one-way ANOVA test are that the populations have equal variances, the factor is categorical, the response is numerical, the populations are assumed to be normal, and the samples are randomly selected and independent. The null hypothesis for a one-way ANOVA with four groups is that the population means are equal. The alternative hypothesis for a one-way ANOVA with three groups is that at least two of the group means are not equal. An ANOVA test is used to compare means of three or more groups.

Step-by-step explanation:

1. The populations are assumed to have equal standard deviations (or variances).
2. The factor is a categorical variable.
3. The response is a numerical variable.
4. Each population from which a sample is taken is assumed to be normal.
5. All samples are randomly selected and independent.

The null hypothesis for a one-way ANOVA test with four groups is that the population means of all four groups are equal.

The alternative hypothesis for a one-way ANOVA test with three groups is that at least two of the group means are not equal.

An ANOVA test is used when comparing means of three or more groups to determine if there is a statistically significant difference among the group means.