Q: A Gallup survey finds the following counts for engagement by generation: Millennials (Engaged: 102, Not Engaged: 193, Actively Disengaged: 55), Gen Xers (Engaged: 109, Not Engaged: 170, Actively Disengaged: 61), Baby Boomers (Engaged: 93, Not Engaged: 134, Actively Disengaged: 53), Traditionalists (Engaged: 14, Not Engaged: 12, Actively Disengaged: 4). What is the expected count of Engaged Millennials under the null hypothesis? $$E = \frac{(Row\ Total) \times (Column\ Total)}{Grand\ Total}$$

$$E = \frac{318 \times 350}{1000} = 111.3$$

Question 1

In an ANOVA experiment with four groups and eight values in each group, the sum of squares among groups is 80 and the sum of squares within groups is 560. What is the mean square among groups ($$MS_{Between}$$)?

$$MS_{Between} = \frac{SS_{Between}}{df_{Between}}$$

Where $$df_{Between} = k - 1$$ and $$k is $$the number of groups.

Accepted Answer

$$MS_{Between} = \frac{80}{3} = 26.67$$

Question 2

A medical facility wants to test if there is a difference in mean emergency room waiting times across four campuses. Which statistical test should be used to compare the means of more than two independent groups?

Accepted Answer

One-way ANOVA

Question 3

Given the following ANOVA summary: $$SS_{Between} = 80$$, $$SS_{Within} = 560$$, $$n = 32 (4 $$groups, 8 per group), what is the F-statistic?

$$F = \frac{MS_{Between}}{MS_{Within}}$$

Where $$MS_{Within} = \frac{SS_{Within}}{df_{Within}}$$ and $$df_{Within} = N - k.$$

Accepted Answer

$$F = \frac{26.67}{20} = 1.33$$

Question 4

A survey of 500 executives in each of five industries found different proportions investing in sensor technology. Which test is most appropriate to determine if the proportions differ among industries?

Accepted Answer

Chi-square test for homogeneity

Question 5

In the context of the Marascuilo procedure, what is its primary use after a significant chi-square test for proportions?

Accepted Answer

To determine which specific groups differ in their proportions

Question 6

A marketing analyst compares the median weekly sales leads from two advertising strategies using independent samples. Which nonparametric test is most appropriate?

Accepted Answer

Mann-Whitney U test

Question 7

Given the following contingency table of engagement by generation, what is the null hypothesis for a chi-square test of independence?

$$H_0$$:$$

Accepted Answer

There is no association between generation and level of engagement.

Question 8

If the p-value for a chi-square test comparing proportions across five industries is 0.03, what is the correct interpretation at $$\alpha = 0.05$$?

Accepted Answer

There is sufficient evidence to conclude that at least one industry differs in proportion.

Question 9

Which of the following is a key assumption of one-way ANOVA?

Accepted Answer

The populations have equal variances.

Question 10

A Gallup survey finds the following counts for engagement by generation: Millennials (Engaged: 102, Not Engaged: 193, Actively Disengaged: 55), Gen Xers (Engaged: 109, Not Engaged: 170, Actively Disengaged: 61), Baby Boomers (Engaged: 93, Not Engaged: 134, Actively Disengaged: 53), Traditionalists (Engaged: 14, Not Engaged: 12, Actively Disengaged: 4). What is the expected count of Engaged Millennials under the null hypothesis?

$$E = \frac{(Row\ Total) 	imes (Column\ Total)}{Grand\ Total}$$

Accepted Answer

$$E = \frac{318 	imes 350}{1000} = 111.3$$

Question 11

Which of the following is NOT a requirement for using the chi-square test for independence?

Accepted Answer

The data are normally distributed.

Question 12

A business wants to test if the variation in waiting times differs among four campuses. Which test is most appropriate?

Accepted Answer

Levene's test for equality of variances

Question 13

If the F-statistic in an ANOVA test is much larger than 1, what does this suggest about the group means?

Accepted Answer

There is evidence that at least one group mean is different.

Question 14

Which of the following best describes the purpose of post-hoc tests in ANOVA?

Accepted Answer

To identify which specific group means are different after finding a significant F-test.

Question 15

A marketing analyst uses the Mann-Whitney U test to compare two advertising strategies. What is the null hypothesis for this test?

Accepted Answer

The distributions of weekly sales leads are the same for both strategies.

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