Question 1

Which of the following is NOT an assumption required for conducting a one-way ANOVA F test?

Accepted Answer

The sample sizes in each group must be equal.

Question 2

In a one-way ANOVA, what does the null hypothesis $$H_0$$ state?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$ = \$$mu_3$$ = \cdots = \mu_c$

Question 3

Suppose you conduct a one-way ANOVA and obtain $$F_{STAT} = 6.2$$ with a critical value $$F_{\alpha} = 4.0 at$$ $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is evidence that at least one mean is different.

Question 4

Which formula correctly represents the total sum of squares (SST) in a one-way ANOVA?

Accepted Answer

$$SST = \sum_{j=1}^{c} \sum_{i=1}^{n_j} (X_{ij} - \overline{X})^2$

Question 5

A researcher wants to compare the mean productivity of employees across four departments. Which statistical test is most appropriate?

Accepted Answer

One-way ANOVA

Question 6

In a one-way ANOVA, how is the F statistic calculated?

Accepted Answer

$$F_{STAT} = \frac{MSA}{MSW}$$

Question 7

Which test is used to check the assumption of homogeneity of variances in ANOVA?

Accepted Answer

Levene's test

Question 8

After rejecting the null hypothesis in a one-way ANOVA, which procedure is commonly used to determine which means are significantly different?

Accepted Answer

Tukey-Kramer multiple comparison procedure

Question 9

In the context of ANOVA, what does 'partitioning the variation' mean?

Accepted Answer

Splitting the total variation into among-group and within-group components.

Question 10

Which of the following is TRUE about the F statistic in ANOVA?

Accepted Answer

It is the ratio of the among-group mean square to the within-group mean square.

Question 11

A company tests three brands of tires for expected mileage. The sample means are 40,000, 42,000, and 39,500 miles. If the absolute mean differences are all greater than the Tukey-Kramer critical range, what can be concluded?

Accepted Answer

At least one brand has a significantly different expected mileage.

Question 12

In a two-way ANOVA, what is the first step in interpreting the results?

Accepted Answer

Determine if the interaction effect is statistically significant.

Question 13

Which formula gives the mean square among groups (MSA) in a one-way ANOVA?

Accepted Answer

$$MSA = \frac{SSA}{c-1}$$

Question 14

Which of the following best describes a completely randomized design in ANOVA?

Accepted Answer

Subjects are assigned randomly to groups and only one factor is studied.

Question 15

In a two-way ANOVA, which term represents the variation due to the interaction between factors A and B?

Accepted Answer

$$SSAB$$

Question 16

A business analyst wants to test the effect of two factors (training method and department) on employee performance. Which statistical method should be used?

Accepted Answer

Two-way ANOVA

Question 17

Which of the following is the correct formula for the mean square within groups (MSW) in a one-way ANOVA?

Accepted Answer

$$MSW = \frac{SSW}{n-c}$$

Question 18

Which of the following statements about the normality assumption in ANOVA is correct?

Accepted Answer

ANOVA is fairly robust to departures from normality, especially with large samples.

Question 19

In the context of ANOVA, what is the purpose of random assignment of subjects to groups?

Accepted Answer

To avoid bias and ensure experimental validity.

Analysis of Variance (ANOVA): One-Way and Two-Way Methods

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