Business Statistics Quiz: One Way Anova

What this quiz covers

This quiz focuses on One Way Anova, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. 6.0 (correct answer)
2. 8.0
3. 54.0
4. 60.0

Question 2

1. 5.00
2. 6.67 (correct answer)
3. 20.00
4. 26.67

Question 3

1. F = 3.56; df₁ = 4, df₂ = 50, providing moderate evidence of differences between store locations (correct answer)
2. F = 3.56; df₁ = 5, df₂ = 55, indicating significant variation in customer satisfaction across all locations
3. F = 0.28; df₁ = 4, df₂ = 50, suggesting no meaningful differences in satisfaction between store locations
4. F = 0.28; df₁ = 5, df₂ = 55, indicating homogeneous satisfaction levels across the retail chain

Question 4

1. 0.40
2. 2.50
3. 5.40 (correct answer)
4. 6.75

Question 5

1. The power of each individual t-test would be lower than the power of a single ANOVA test, increasing the chance of a Type II error.
2. It inflates the family-wise Type I error rate, substantially increasing the probability of incorrectly finding a significant difference. (correct answer)
3. Two-sample t-tests are only valid when the sample sizes for all groups are exactly equal, which may not be the case.
4. The process of running six separate tests is less efficient and more computationally intensive than a single ANOVA.

Question 6

1. 0.20; The training programs explain 20% of the variance in employee performance scores. (correct answer)
2. 0.25; The training programs explain 25% of the variance in employee performance scores.
3. 4.00; The variance between training programs is 4 times the variance within the programs.
4. 0.80; 80% of the variance in performance scores is due to factors other than the training programs.

Question 7

1. Exactly 0 (correct answer)
2. Exactly 1
3. A value that depends on the total sample size
4. A negative value, indicating no difference

Question 8

1. $H_0: \mu_1 = \mu_2 = \mu_3$ versus $H_a: \mu_1 \neq \mu_2 \neq \mu_3$
2. $H_0: \bar{x}_1 = \bar{x}_2 = \bar{x}_3$ versus $H_a: \bar{x}_1 \neq \bar{x}_2 \neq \bar{x}_3$
3. $H_0: \mu_1 = \mu_2 = \mu_3$ versus $H_a:$ At least one population mean is different. (correct answer)
4. $H_0:$ At least one population mean is different versus $H_a: \mu_1 = \mu_2 = \mu_3$

Question 9

1. The F-statistic would decrease, making a significant result less likely.
2. The F-statistic would increase, making a significant result more likely. (correct answer)
3. The F-statistic would remain unchanged because it is a ratio of variances.
4. The effect on the F-statistic cannot be determined without knowing the sample sizes.

Question 10

1. Reject H₀ because the calculated F-statistic of 6.00 is greater than the critical value.
2. Fail to reject H₀ because the calculated F-statistic of 4.50 is greater than the critical value.
3. Fail to reject H₀ because the calculated F-statistic of 0.33 is less than the critical value.
4. Reject H₀ because the calculated F-statistic of 4.50 is greater than the critical value. (correct answer)

Question 11

1. The area under the F-distribution curve to the left of the calculated F-statistic.
2. Twice the area under the F-distribution curve to the right of the calculated F-statistic, to account for a two-tailed test.
3. The height of the F-distribution curve at the point corresponding to the calculated F-statistic.
4. The area under the F-distribution curve to the right of the calculated F-statistic. (correct answer)

Question 12

1. The company can conclude with 95% confidence that the mean click-through rates for all four ad creatives are identical.
2. There is insufficient evidence to conclude that there are any differences in the mean click-through rates among the four ad creatives. (correct answer)
3. The test proves that there is no difference in the effectiveness of the ad creatives.
4. A Type II error has occurred, and the company should re-run the test with a different statistical method.

Question 13

1. The p-value is greater than 0.05.
2. The p-value cannot be estimated without knowing the exact sample size.
3. The p-value is exactly 0.05.
4. The p-value is less than 0.05. (correct answer)

Question 14

1. F = 15.00; this provides very strong evidence for differences since it greatly exceeds typical critical values
2. F = 30.00; this suggests possible differences, but the unequal sum of squares indicates assumption violations
3. F = 30.00; this provides extremely strong evidence since it represents a very large effect size
4. F = 15.00; this provides moderate evidence, but interpretation depends on the chosen significance level and critical value (correct answer)

Question 15

1. 150
2. 450 (correct answer)
3. 600
4. Cannot be determined without the total sample size.

Question 16

1. The variance of productivity in one department is double the variance of another, but sample sizes are large and equal (n=100 per department).
2. The sample means of the five departments are found to be very close to one another, resulting in a low F-statistic.
3. Productivity data for two of the departments are heavily skewed, and the sample sizes are small (n=12 per department). (correct answer)
4. The overall distribution of productivity scores from all 60 employees combined appears to be slightly bimodal.

Question 17

1. Conclude that the supplier with the highest sample mean breaking strength is definitively the best.
2. Re-run the analysis with a larger sample size to confirm the result's validity.
3. Perform post-hoc tests, such as Tukey's HSD, to identify which specific pairs of suppliers have different mean breaking strengths. (correct answer)
4. Accept the alternative hypothesis that all five suppliers have different mean breaking strengths from one another.

Question 18

1. The test results are invalid because the F-statistic cannot be less than 1.
2. The null hypothesis will be rejected, regardless of the significance level.
3. The variance within groups is smaller than the variance between groups.
4. The null hypothesis will not be rejected at any conventional significance level. (correct answer)

Question 19

1. There is a 2.3% probability that the null hypothesis of equal means is true.
2. There is a 2.3% chance of observing sample mean differences as large or larger than the ones found, if the service centers truly have the same mean satisfaction score. (correct answer)
3. There is a 97.7% probability that there is a real difference in the mean satisfaction scores among the four service centers.
4. The results prove that all four service centers have different mean satisfaction scores from one another.

Question 20

1. The test provides strong evidence against equal means since the F-statistic exceeds the degrees of freedom ratio
2. The test fails to provide sufficient evidence of differences at the 0.01 level, but may show significance at α = 0.05 (correct answer)
3. The test is inconclusive because the sample sizes are unequal, violating a key ANOVA assumption
4. The test shows marginal significance since the F-statistic is close to the critical value within one standard error