What is the primary purpose of using ANOVA instead of multiple *t*-tests when comparing three or more group means?

• To reduce the risk of Type I error by avoiding multiple comparisons.

• To simplify calculations by using a single test.

• To eliminate the need for variance calculations.

• To allow comparisons of non-normal distributions.

In a one-way ANOVA, if the between-group variance (MSB) is significantly larger than the within-group variance (MSW), what conclusion can be drawn?

• All group means are equal.

• At least one group mean differs from the others.

• The variances of all groups are equal.

• The sample sizes are too small.

For a one-way ANOVA with 4 groups (k = 4) and a total sample size of 20 (N = 20), what are the degrees of freedom for the numerator (d.f.N.) and denominator (d.f.D.)?

An ANOVA test yields an F-ratio of 1.2. If the critical F-value at α = 0.05 is 3.5, what is the correct decision?

• Reject the null hypothesis; group means differ.

• Fail to reject the null hypothesis; no evidence of difference.

• Conclude that all group means are identical.

• Increase the sample size and retest.

Which of the following is not an assumption of one-way ANOVA?

• A) Populations are normally distributed.

• B) Samples are independent.

• C) Population variances are equal (homoscedasticity).

• D) Data must be measured on a nominal scale.