PRACTICE QUESTIONS

Questionnaire

1. The one-sample t-test assumes that the data are normally distributed.

   • Answer: True

   • Explanation: A one-sample t-test is parametric and assumes normality.

2. Welch's t-test is a parametric test used when the variances of two groups are unequal.

   • Answer: True

   • Explanation: Welch’s t-test does not assume equal variances, unlike the independent t-test.

3. The Mann-Whitney U test is appropriate for ordinal data.

   • Answer: True

   • Explanation: The Mann-Whitney U test is non-parametric and works with ordinal or continuous data.

4. A normality test evaluates whether data follow a normal distribution.

   • Answer: True

   • Explanation: Normality tests (e.g., Shapiro-Wilk, Kolmogorov-Smirnov) assess the normality assumption.

5. Levene's test is used to test the equality of variances between two or more groups.

   • Answer: True

   • Explanation: Levene’s test checks homogeneity of variances, which is a key assumption for parametric tests.

6. Homogeneity of variances means all groups have the same mean.

   • Answer: False

   • Explanation: Homogeneity refers to variances, not means.

7. The two-sample t-test assumes that the samples are independent of each other.

   • Answer: True

   • Explanation: Independence is a core assumption of the two-sample t-test.

8. ANOVA can only be used when there are exactly two groups.

   • Answer: False

   • Explanation: ANOVA is used when comparing the means of three or more groups.

9. The F-test in ANOVA compares the variability between group means to variability within groups.

   • Answer: True

   • Explanation: This is the essence of the F-test in one-way ANOVA.

10. One-way ANOVA assumes that the dependent variable is ordinal.

• Answer: False

• Explanation: One-way ANOVA is parametric and assumes the dependent variable is continuous.

11. The Kruskal-Wallis test is the non-parametric equivalent of one-way ANOVA.

• Answer: True

• Explanation: Kruskal-Wallis is used for ordinal or non-normal continuous data.

12. The DSCF post-hoc test is used after Kruskal-Wallis to identify which groups differ.

• Answer: True

• Explanation: The Dwass-Steel-Critchlow-Fligner test is a post-hoc test for Kruskal-Wallis.

13. Pearson’s rr measures the strength and direction of a linear relationship between two variables.

• Answer: True

• Explanation: Pearson’s rr is parametric and assumes linearity and normality.

14. Spearman’s ρ\rho is a non-parametric test that evaluates monotonic relationships.

• Answer: True

• Explanation: Spearman’s ρ\rho is used when data are ordinal or not normally distributed.

15. The chi-square test is used for testing relationships between two categorical variables.

• Answer: True

• Explanation: The chi-square test is non-parametric and evaluates categorical data.

16. ANOVA assumes homogeneity of variances.

• Answer: True

• Explanation: Homogeneity is a key assumption for one-way ANOVA.

17. The Mann-Whitney U test requires normal distribution of data.

• Answer: False

• Explanation: The Mann-Whitney U test is non-parametric and does not require normality.

18. Welch’s t-test is more robust than a standard t-test when variances are unequal.

• Answer: True

• Explanation: Welch’s t-test is designed for unequal variances.

19. A normality test is unnecessary for non-parametric tests like the Kruskal-Wallis test.

• Answer: True

• Explanation: Non-parametric tests do not rely on normality assumptions.

20. Pearson’s rr can be used with ordinal data.

• Answer: False

• Explanation: Pearson’s rr is parametric and assumes continuous, interval data.

21. The Kruskal-Wallis test assumes that the data are independent within groups.

• Answer: True

• Explanation: Independence is a common assumption even for non-parametric tests.

22. Levene’s test is non-parametric.

• Answer: False

• Explanation: Levene’s test is a parametric test for equality of variances.

23. Spearman’s ρ\rho is suitable for non-linear relationships.

• Answer: True

• Explanation: Spearman’s ρ\rho evaluates monotonic (not necessarily linear) relationships.

24. Welch’s t-test can be used for paired samples.

• Answer: False

• Explanation: Welch’s t-test is designed for independent samples.

25. Homogeneity of variances is tested before performing a t-test or ANOVA.

• Answer: True

• Explanation: Homogeneity is an assumption for these tests.

26. The chi-square test assumes that expected frequencies in each cell are at least 5.

• Answer: True

• Explanation: This is a common assumption of the chi-square test.

27. Kruskal-Wallis is more powerful than ANOVA when data are normally distributed.

• Answer: False

• Explanation: ANOVA is more powerful for normal data, while Kruskal-Wallis is better for non-normal data.

28. Pearson’s rr assumes that both variables are normally distributed.

• Answer: True

• Explanation: Pearson’s rr is parametric and assumes normality

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29. F-tests can be used to compare variances of more than two groups.

• Answer: True

• Explanation: The F-test in ANOVA compares variances across multiple groups.

30. The Mann-Whitney U test is equivalent to the t-test for medians.

• Answer: True

• Explanation: While not strictly comparing medians, Mann-Whitney is often viewed as a median test in practice.

Situational Questions

1. You are testing whether the mean weight of a specific species of fish in a lake differs from 3 kg. You should use a one-sample t-test if the weights are normally distributed.

   • Answer: True

   • Explanation: The one-sample t-test is used to compare the sample mean to a known value under the assumption of normality.

2. A researcher wants to compare the effectiveness of two fertilizers on crop yield. The variances of the yield data are unequal, so the appropriate test is Welch's t-test.

   • Answer: True

   • Explanation: Welch’s t-test is suitable for comparing two groups with unequal variances.

3. You are analyzing customer satisfaction rankings (ordinal data) from two different stores. The Mann-Whitney U test is the correct choice.

   • Answer: True

   • Explanation: Mann-Whitney U is non-parametric and ideal for ordinal data.

4. A team wants to compare test scores across three schools. They assume normal distribution and homogeneity of variances. One-way ANOVA is an appropriate test for this situation.

   • Answer: True

   • Explanation: One-way ANOVA is parametric and compares the means of three or more groups under these assumptions.

5. You need to determine if students’ test scores improve after attending a review session. A two-sample t-test is the correct approach.

   • Answer: False

   • Explanation: A paired t-test is appropriate because the data are dependent (before-and-after measurements for the same students).

6. A biologist compares the levels of dissolved oxygen across four different lakes. The data are skewed, so the appropriate test is the Kruskal-Wallis test.

   • Answer: True

   • Explanation: Kruskal-Wallis is non-parametric and suitable for non-normal data when comparing multiple groups.

7. You are testing if males and females have different preferences for a type of product, based on a categorical survey (e.g., yes/no). A chi-square test is appropriate for this analysis.

   • Answer: True

   • Explanation: The chi-square test is used for categorical data to test relationships or differences.

8. A researcher is evaluating the correlation between age and blood pressure, assuming the data are normally distributed. Spearman’s rho is the correct choice.

   • Answer: False

   • Explanation: Pearson’s rr is used for normally distributed data. Spearman’s rho is non-parametric and used for ordinal or non-linear data.

9. You want to test if two groups of students perform equally on an exam, but their scores show a significant difference in variances. Levene's test should be performed before deciding on a t-test.

   • Answer: True

   • Explanation: Levene’s test checks for equality of variances, which helps determine whether to use a standard t-test or Welch’s t-test.

10. An organization wants to test if four training programs produce the same improvement in productivity. Data are normally distributed, and variances are equal. The F-test in ANOVA is appropriate.

• Answer: True

• Explanation: One-way ANOVA (using the F-test) is used for comparing the means of four groups under these assumptions.