Hypothesis testing: z-test, t-test, ANOVA, chi-square, Mann-Whitney, Kruskal-Wallis, rank correlation - One Line Questions

1. Spearman's rank correlation coefficient (ρ) ranges from: — -1 to +1
2. What is the significance level (alpha) typically set to in social science research? — 0.05
3. A researcher uses a z-test for a single proportion. The sample size is 40, and the population standard deviation is unknown. What is the most likely error in this approach? — A t-test should have been used instead of a z-test.
4. A Type II Error occurs when: — A false null hypothesis is not rejected
5. If Spearman's rho is calculated to be 0.95, what does this indicate? — A strong positive monotonic relationship
6. What is the primary difference between a z-test and a t-test? — A z-test uses population standard deviation, while a t-test uses sample standard deviation.
7. In a one-way ANOVA, if the p-value is less than the significance level (e.g., 0.05), what conclusion can be drawn? — At least one group mean is significantly different from the others
8. In a Kruskal-Wallis test, the null hypothesis is that: — The distributions of the groups are identical
9. In ANOVA, the null hypothesis states that: — All group means are equal
10. Which type of hypothesis states that there is no significant difference or relationship between variables? — Null Hypothesis (H0)
11. The Chi-square distribution is: — Positively skewed and its shape depends on the degrees of freedom
12. ANOVA (Analysis of Variance) is a statistical technique used to: — Compare the means of three or more independent groups
13. A paired t-test is used when: — Comparing the means of two related samples (e.g., before and after treatment)
14. A chi-square (χ²) test is primarily used for: — Testing the independence of two categorical variables
15. The chi-square goodness-of-fit test is used to: — Determine if a sample distribution matches a hypothesized population distribution
16. When conducting a z-test, if the calculated z-score falls within the rejection region, we: — Reject the null hypothesis
17. If a p-value is 0.02 and the significance level (alpha) is 0.05, what is the decision regarding the null hypothesis? — Reject the null hypothesis
18. The Kruskal-Wallis H test is a non-parametric alternative to which parametric test? — One-way ANOVA
19. The Wilcoxon signed-rank test is the non-parametric equivalent of which test? — Paired t-test
20. A researcher wants to test if there is a significant difference in the effectiveness of three different teaching methods on student performance. Which test is most appropriate? — One-way ANOVA
21. A t-test is based on the t-distribution, which: — Is flatter and has heavier tails than the standard normal distribution
22. Which non-parametric test is suitable for comparing two related samples when the assumptions for a paired t-test are not met? — Wilcoxon signed-rank test
23. Which of the following tests is MOST sensitive to outliers? — Independent samples t-test
24. Which of the following is a parametric test? — Independent samples t-test
25. The F-statistic in ANOVA is calculated as the ratio of: — Mean Square Between (MSB) to Mean Square Within (MSW)
26. The Mann-Whitney U test is a non-parametric alternative to which parametric test? — Independent samples t-test
27. Which test would be appropriate to determine if there is an association between gender (Male/Female) and preference for a political party (Party A/Party B/Party C)? — Chi-square test of independence
28. When comparing the means of two independent groups with unequal variances, which version of the t-test is often recommended? — Welch's t-test
29. The degrees of freedom for a chi-square test of independence with 'r' rows and 'c' columns is calculated as: — (r - 1) * (c - 1)
30. Which assumption is CRUCIAL for the validity of a chi-square test of independence? — The expected frequencies in each cell are not too small (often a minimum of 5)
31. What is the primary assumption of the Mann-Whitney U test? — The two samples are independent and come from distributions with the same shape
32. Rank correlation, such as Spearman's rho, is used to measure: — The strength and direction of the monotonic relationship between two ranked variables
33. The Mann-Whitney U test compares: — The distributions of two independent groups
34. What is the critical value in hypothesis testing? — The threshold value that separates the rejection region from the non-rejection region
35. A z-test is appropriate when: — The population standard deviation is known or the sample size is large (n > 30)
36. Which of the following is a key assumption for a t-test for independent samples? — The data in both groups are approximately normally distributed
37. The power of a statistical test is defined as: — The probability of correctly rejecting a false null hypothesis
38. A p-value in hypothesis testing represents: — The probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true
39. Which of the following is NOT an assumption for the Kruskal-Wallis H test? — The distributions of the groups have equal medians
40. What does the 'degrees of freedom' represent in a t-test? — The number of independent pieces of information available to estimate a parameter
41. The null hypothesis for a chi-square test of independence states that: — The two categorical variables are independent
42. In the context of ANOVA, 'Sum of Squares Within' (SSW) measures: — The variability of scores of individuals within their respective groups around their group mean
43. In the context of ANOVA, 'Sum of Squares Between' (SSB) measures: — The variability of scores around the grand mean that is attributable to the differences between group means
44. When is a z-test for proportions used? — To test a hypothesis about a single population proportion when the sample size is large
45. What is the primary goal of post-hoc tests in ANOVA? — To control the family-wise error rate when conducting multiple comparisons between group means
46. What is the primary purpose of hypothesis testing in statistics? — To make decisions about population claims based on sample data
47. The probability of rejecting a true null hypothesis is known as: — Type I Error (alpha)
48. When using Spearman's rank correlation, what is the most appropriate situation? — When the data are ordinal or when the relationship between two continuous variables is monotonic but not necessarily linear
49. Which test is used to compare the means of two independent groups when the population standard deviation is unknown and sample sizes are small? — Independent samples t-test
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