Question 1

Which of the following best describes the main purpose of a one-way ANOVA?

Accepted Answer

To compare the means of more than two populations using a single hypothesis test.

Question 2

Suppose a researcher wants to compare the average test scores of students from four different teaching methods. Which statistical test should they use?

Accepted Answer

One-way ANOVA

Question 3

What is the null hypothesis $$H_0 in a $$one-way ANOVA comparing $$k$$ groups?

Accepted Answer

$$\mu_1$ = \mu_2$ = \cdots = \mu_k$$

Question 4

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

Accepted Answer

The population means are equal

Question 5

Why is it problematic to use multiple two-sample t-tests instead of ANOVA when comparing more than two groups?

Accepted Answer

It increases the familywise error rate, making it more likely to incorrectly reject at least one true null hypothesis.

Question 6

Given the following ANOVA summary: $$SS_{total} = 1000$$, $$SS_{within} = 700$$, what is $$SS_{between}$$?

Accepted Answer

$$SS_{between} = 300$$

Question 7

Which formula correctly calculates the F-statistic in a one-way ANOVA?

Accepted Answer

$$F = \frac{MS_{between}}{MS_{within}}$$

Question 8

A researcher performs a one-way ANOVA and obtains $$F = 0.95$$ with a p-value of $$0.45. $$What is the correct interpretation?

Accepted Answer

There is not enough evidence to conclude that the group means are different.

Question 9

Which of the following best describes the familywise error rate?

Accepted Answer

The probability of making at least one Type I error across multiple hypothesis tests.

Question 10

If the largest group standard deviation is 10 and the smallest is 4, does the data meet the ANOVA equal variance condition?

Accepted Answer

No, because $$\frac{10}{4} = 2.5 \u003e 2$$

Question 11

Which of the following is the correct formula for the total sum of squares in ANOVA?

Accepted Answer

$$SS_{total} = \sum (x - \bar{x})^2$

Question 12

In an ANOVA table, what does the 'Within' sum of squares ($$SS_{within}) $$represent?

Accepted Answer

The unexplained variation due to differences within each group.

Question 13

A clinical trial compares the effect of three diets on weight loss. The ANOVA yields $$F = 5.2$$ and $$p = 0.008. $$What should the researcher conclude at $$\alpha = 0.05$$?

Accepted Answer

At least one diet leads to a different mean weight loss compared to the others.

Question 14

Which of the following is a condition that must be checked before performing a one-way ANOVA?

Accepted Answer

The samples are independent of each other.

Question 15

Given $$k = 4$$ groups and a total of $$N = 40$$ observations, what are the degrees of freedom for 'between', 'within', and 'total' in the ANOVA table?

Accepted Answer

'Between': $$3$$, 'Within': $$36$$, 'Total': $$39$$

Question 16

Which scenario would most likely result in a large F-statistic in ANOVA?

Accepted Answer

Large variation between group means and small variation within groups.

Question 17

If the null hypothesis in ANOVA is true, what value do we expect for the F-statistic?

Accepted Answer

Approximately 1

Question 18

A company tests three brands of fertilizer on plant growth. The ANOVA results show $$p = 0.12. $$What is the correct conclusion at $$\alpha = 0.05$$?

Accepted Answer

There is not enough evidence to conclude that the fertilizers differ in their effect on plant growth.

Question 19

Which of the following best explains why ANOVA is preferred over multiple t-tests when comparing several means?

Accepted Answer

ANOVA controls the familywise error rate, reducing the chance of Type I errors.

Chapter 11-A

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