Q: Which formula correctly represents the F-test statistic in one-way ANOVA?

$$F = \dfrac{\text{MST}}{\text{MSE}}$$

Question 1

Which of the following is NOT a requirement for performing a one-way ANOVA test?

Accepted Answer

Each sample must have the same sample size.

Question 2

Why is it inappropriate to test $$H_0$$: \$$mu_1$$ = \$$mu_2$$ = \$$mu_3 by $$conducting three separate hypothesis tests at $$\alpha = 0.05$$?

Accepted Answer

It increases the probability of making a Type I error above $$\alpha.$$

Question 3

Given three samples with standard deviations $$0.022$$, $$0.024$$, and $$0.014$$, does the requirement of equal population variances hold for one-way ANOVA?

Accepted Answer

Yes, because the largest standard deviation is less than twice the smallest.

Question 4

What is the null hypothesis in a one-way ANOVA test comparing $$k$$ means?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$ = \cdots = \mu_k$$

Question 5

Which formula correctly represents the F-test statistic in one-way ANOVA?

Accepted Answer

$$F = \dfrac{	ext{MST}}{	ext{MSE}}$$

Question 6

A researcher performs a one-way ANOVA and obtains $$F_0 = 1.25$ with a critical value F$$_{crit} = 3.32$$ at $$\alpha = 0.05$$. What is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence to say the means are different.

Question 7

In the context of ANOVA, what does the 'between-sample variability' measure?

Accepted Answer

The variability among the sample means.

Question 8

Which of the following is TRUE about the robustness of one-way ANOVA procedures?

Accepted Answer

ANOVA is robust to small departures from normality and equal variances, especially with equal sample sizes.

Question 9

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

Accepted Answer

Tukey's test

Question 10

Given $$s^2 = 28.7$, n_1$ = n_2$ = n_3$ = 9$$, and sample means $$x_1 = 131.8$, x_2$ = 142.9$$, $$x_3 = 135.0$, what is the test statistic for comparing x_2$ and x_1$ using Tukey’s test?

Accepted Answer

$$q_0$$ = \dfrac{11.1}{\sqrt{28.7 \left(\dfrac{2}{9}\right)}} = 6.22$$

Question 11

In a randomized complete block design, what is the primary purpose of blocking?

Accepted Answer

To remove experimental error and reduce mean square error.

Question 12

Which of the following is the correct formula for the standard error used in Tukey’s test for comparing two means?

Accepted Answer

$$SE = \sqrt{s^2$ \left( \dfrac{1}{n_1$} + \dfrac{1}{n_2$} \right)}$$

Question 13

A rice farmer uses a randomized complete block design to test four fertilizers. The ANOVA output shows $$F = 22.40$$ for fertilizer and $$F = 30.20$$ for row, both with $$P \u003c 0.001. $$What is the correct interpretation?

Accepted Answer

There is a significant difference in fruiting period among the fertilizers.

Question 14

Which of the following best describes the decision rule for the classical method in one-way ANOVA?

Accepted Answer

Reject $$H_0 if$$ $$F_{test} \u003e F_{critical}$$

Question 15

If the largest sample standard deviation is 0.024 and the smallest is 0.014, does the equal variance assumption for ANOVA hold?

Accepted Answer

Yes, because $$0.024 \leq 2 	imes 0.014$$

Question 16

Which of the following is NOT a step in performing Tukey’s test after a significant ANOVA result?

Accepted Answer

Test whether the block means are significantly different.

Question 17

In the context of ANOVA, what does the mean square error (MSE) estimate?

Accepted Answer

The variance within the samples.

Question 18

Suppose you have three groups with equal sample sizes and you want to check the equal variance assumption for ANOVA. Which rule should you use?

Accepted Answer

The largest sample standard deviation should be no more than twice the smallest.

Comparing Three or More Means: One-Way ANOVA and Block Designs

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