Question 1

Which of the following best describes the purpose of using dummy variables in an ANOVA regression model when comparing several groups?

Accepted Answer

To allow the regression model to compare the mean of each group to a baseline group.

Question 2

Suppose you are comparing the yields of five wheat varieties using ANOVA. What is the null hypothesis for the F-test?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$ = \$$mu_3$$ = \$$mu_4$$ = \$$mu_5$$

Question 3

In the regression model $$\hat{y} = b_0$ + b_1$ D(Endurance)$$, what does $$b_1$$ represent?

Accepted Answer

The difference in average yield between Endurance and the baseline group.

Question 4

Given the regression output: Intercept = 14.05, $$b_1 ($$Endurance) = 5.53, what is the predicted yield for Endurance?

Accepted Answer

$$19.58$$

Question 5

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

Accepted Answer

The means of all groups must be equal.

Question 6

If the p-value for the F-test in an ANOVA table is less than 0.05, what is the appropriate conclusion?

Accepted Answer

Reject the null hypothesis; at least one group mean is different.

Question 7

Why do we use Tukey confidence intervals in multiple comparisons after ANOVA?

Accepted Answer

To control the overall Type I error rate across all pairwise comparisons.

Question 8

A Tukey 95% confidence interval for the difference in yield between Endurance and Hatcher is $$2.04 \pm 6.07. $$What does this interval suggest?

Accepted Answer

The difference is not statistically significant.

Question 9

If the residuals from an ANOVA regression appear nearly normal in a normal quantile plot, what does this indicate?

Accepted Answer

The assumption of normality is satisfied.

Question 10

In an ANOVA regression with five groups, how many dummy variables are needed?

Accepted Answer

4

Question 11

Which of the following best explains why the Bonferroni method adjusts the significance level for multiple comparisons?

Accepted Answer

To reduce the probability of making at least one Type I error across all comparisons.

Question 12

Suppose the standard deviations of yields for five wheat varieties are within a factor of 3 to 1. What does this suggest about the ANOVA assumptions?

Accepted Answer

The equal variances assumption is likely satisfied.

Question 13

A farmer wants to know if the type of wheat variety affects yield. Which statistical method is most appropriate?

Accepted Answer

One-way ANOVA regression with dummy variables for each variety.

Question 14

If the regression model for yield is $$\hat{y} = 11.68 + 7.90 D(Endurance)$$, what is the predicted yield for Endurance?

Accepted Answer

$$19.58$$

Question 15

Which of the following is a consequence of having unbalanced group sizes in ANOVA?

Accepted Answer

Confidence intervals for pairwise comparisons will have different widths.

Question 16

In the context of ANOVA, what does a significant F-statistic indicate?

Accepted Answer

At least one group mean is different from the others.

Question 17

Which of the following best describes a balanced experiment in ANOVA?

Accepted Answer

Each group has the same number of observations.

Question 18

If the regression output for $$D(Hatcher) is 5.86 $$with a p-value of 0.0087, what does this mean?

Accepted Answer

Hatcher's mean yield is significantly higher than the baseline group.

Question 19

Which of the following is the correct formula for the ANOVA regression model with four dummy variables?

Accepted Answer

$$y = b_0$ + b_1$ D(Endurance) + b_2$ D(Hatcher) + b_3$ D(NuHills) + b_4$ D(Ripper) + \varepsilon$$

Ch. 26 Analysis of Variance (ANOVA): Comparing Several Groups in Business Statistics

Guida di studio - Domande di pratica