Hypothesis testing: z-test, t-test, ANOVA, chi-square, Mann-Whitney, Kruskal-Wallis, rank correlation - Question Bank

1. If a p-value is 0.02 and the significance level (alpha) is 0.05, what is the decision regarding the null hypothesis?
A) Fail to reject the null hypothesis
B) Reject the null hypothesis
C) The result is inconclusive
D) The alternative hypothesis is accepted
2. When using Spearman's rank correlation, what is the most appropriate situation?
A) When the relationship between two variables is expected to be strictly linear
B) When the data are ordinal or when the relationship between two continuous variables is monotonic but not necessarily linear
C) When testing for differences in means between two independent groups
D) When assessing the independence of two categorical variables
3. The Chi-square distribution is:
A) Always symmetric
B) Always negative
C) Positively skewed and its shape depends on the degrees of freedom
D) Identical to the normal distribution
4. What is the primary goal of post-hoc tests in ANOVA?
A) To determine if the overall ANOVA is significant
B) To control the family-wise error rate when conducting multiple comparisons between group means
C) To calculate the F-statistic
D) To test the equality of variances between groups
5. 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) A t-test should have been used instead of a z-test.
B) The sample size is too large for a z-test.
C) The population standard deviation is not needed for a z-test.
D) A chi-square test should have been used.
6. Which of the following is a parametric test?
A) Mann-Whitney U test
B) Kruskal-Wallis H test
C) Independent samples t-test
D) Chi-square test
7. In a Kruskal-Wallis test, the null hypothesis is that:
A) All group medians are equal
B) All group means are equal
C) The distributions of the groups are identical
D) The variances of the groups are equal
8. When comparing the means of two independent groups with unequal variances, which version of the t-test is often recommended?
A) Pooled variance t-test
B) Welch's t-test
C) Paired t-test
D) One-sample t-test
9. 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)?
A) Paired t-test
B) ANOVA
C) Chi-square test of independence
D) Z-test for proportions
10. The power of a statistical test is defined as:
A) The probability of making a Type I error
B) The probability of making a Type II error
C) The probability of correctly rejecting a false null hypothesis
D) The probability of failing to reject a true null hypothesis
11. A Type II Error occurs when:
A) A true null hypothesis is rejected
B) A false null hypothesis is rejected
C) A false null hypothesis is not rejected
D) A true null hypothesis is not rejected
12. What is the significance level (alpha) typically set to in social science research?
A) 0.01
B) 0.05
C) 0.10
D) 0.50
13. Which of the following tests is MOST sensitive to outliers?
A) Mann-Whitney U test
B) Kruskal-Wallis H test
C) Independent samples t-test
D) Chi-square test
14. If Spearman's rho is calculated to be 0.95, what does this indicate?
A) A weak negative monotonic relationship
B) A strong positive monotonic relationship
C) No monotonic relationship
D) A weak positive linear relationship
15. The Mann-Whitney U test compares:
A) The means of two independent groups
B) The medians of two independent groups
C) The variances of two independent groups
D) The distributions of two independent groups
16. Which assumption is CRUCIAL for the validity of a chi-square test of independence?
A) The data are continuous
B) The expected frequencies in each cell are not too small (often a minimum of 5)
C) The samples are dependent
D) The population follows a normal distribution
17. In the context of ANOVA, 'Sum of Squares Within' (SSW) measures:
A) The variability of scores between groups
B) The variability of scores around the grand mean that is attributable to the differences between group means
C) The total variability in the data
D) The variability of scores of individuals within their respective groups around their group mean
18. In the context of ANOVA, 'Sum of Squares Between' (SSB) measures:
A) The variability of scores within each group
B) The variability of scores around the grand mean that is attributable to the differences between group means
C) The total variability in the data
D) The variability due to random error
19. What is the primary difference between a z-test and a t-test?
A) A z-test uses population standard deviation, while a t-test uses sample standard deviation.
B) A z-test is for small samples, while a t-test is for large samples.
C) A z-test assumes normal distribution, while a t-test does not.
D) A z-test compares means, while a t-test compares variances.
20. When conducting a z-test, if the calculated z-score falls within the rejection region, we:
A) Fail to reject the null hypothesis
B) Reject the null hypothesis
C) Conclude that the alternative hypothesis is false
D) Increase the sample size
21. 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?
A) Independent samples t-test
B) Chi-square test
C) One-way ANOVA
D) Paired t-test
22. The Wilcoxon signed-rank test is the non-parametric equivalent of which test?
A) Independent samples t-test
B) Paired t-test
C) One-way ANOVA
D) Chi-square test
23. Which non-parametric test is suitable for comparing two related samples when the assumptions for a paired t-test are not met?
A) Mann-Whitney U test
B) Wilcoxon signed-rank test
C) Kruskal-Wallis H test
D) Spearman's rho
24. The chi-square goodness-of-fit test is used to:
A) Determine if two categorical variables are independent
B) Compare the means of three or more groups
C) Determine if a sample distribution matches a hypothesized population distribution
D) Test for differences in proportions between two groups
25. A p-value in hypothesis testing represents:
A) The probability of the null hypothesis being true
B) The probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true
C) The significance level chosen by the researcher
D) The effect size of the difference between groups
26. In a one-way ANOVA, if the p-value is less than the significance level (e.g., 0.05), what conclusion can be drawn?
A) All group means are equal
B) There is no significant difference between any of the group means
C) At least one group mean is significantly different from the others
D) The variances of the groups are not equal
27. Which of the following is a key assumption for a t-test for independent samples?
A) The population standard deviations are known
B) The two samples are dependent
C) The data in both groups are approximately normally distributed
D) The sample sizes are very small (n < 10)
28. When is a z-test for proportions used?
A) To compare the means of two large independent samples
B) To test a hypothesis about a single population proportion when the sample size is large
C) To compare the variances of two populations
D) To test for normality of data
29. Spearman's rank correlation coefficient (ρ) ranges from:
A) -1 to +1
B) 0 to +1
C) -∞ to +∞
D) 0 to 100
30. Rank correlation, such as Spearman's rho, is used to measure:
A) The linear relationship between two continuous variables
B) The strength and direction of the monotonic relationship between two ranked variables
C) The difference in means between two groups
D) The association between two categorical variables
31. Which of the following is NOT an assumption for the Kruskal-Wallis H test?
A) The samples are independent
B) The dependent variable is measured on at least an ordinal scale
C) The distributions of the groups have equal medians
D) The distributions of the groups have the same shape
32. The Kruskal-Wallis H test is a non-parametric alternative to which parametric test?
A) Independent samples t-test
B) Paired t-test
C) One-way ANOVA
D) Two-way ANOVA
33. What is the primary assumption of the Mann-Whitney U test?
A) The data are normally distributed
B) The population variances are equal
C) The two samples are independent and come from distributions with the same shape
D) The data are ordinal or interval scale
34. The Mann-Whitney U test is a non-parametric alternative to which parametric test?
A) Paired t-test
B) Independent samples t-test
C) One-way ANOVA
D) Chi-square test
35. The degrees of freedom for a chi-square test of independence with 'r' rows and 'c' columns is calculated as:
A) r * c
B) (r - 1) * (c - 1)
C) r + c - 1
D) (r - 1) + (c - 1)
36. The null hypothesis for a chi-square test of independence states that:
A) The two categorical variables are dependent
B) The two categorical variables are independent
C) All observed frequencies are equal to expected frequencies
D) There is a significant difference in observed frequencies
37. A chi-square (χ²) test is primarily used for:
A) Comparing means of two or more groups
B) Testing the independence of two categorical variables
C) Estimating population variance
D) Testing hypotheses about population proportions
38. The F-statistic in ANOVA is calculated as the ratio of:
A) Mean Square Within (MSW) to Mean Square Between (MSB)
B) Mean Square Between (MSB) to Mean Square Within (MSW)
C) Total Sum of Squares (SST) to Degrees of Freedom Total (DFT)
D) Sum of Squares Between (SSB) to Sum of Squares Within (SSW)
39. In ANOVA, the null hypothesis states that:
A) All group variances are equal
B) At least one group mean is different from the others
C) All group means are equal
D) There is no variance within any group
40. ANOVA (Analysis of Variance) is a statistical technique used to:
A) Compare the means of exactly two groups
B) Test for the association between two categorical variables
C) Compare the means of three or more independent groups
D) Determine the correlation between two continuous variables
41. A paired t-test is used when:
A) Comparing means of two independent groups
B) Comparing the means of two related samples (e.g., before and after treatment)
C) Comparing more than two group means
D) Testing for association between categorical variables
42. What does the 'degrees of freedom' represent in a t-test?
A) The total number of observations
B) The number of independent pieces of information available to estimate a parameter
C) The number of groups being compared
D) The significance level chosen for the test
43. A t-test is based on the t-distribution, which:
A) Is identical to the standard normal distribution
B) Is flatter and has heavier tails than the standard normal distribution
C) Is skewed to the right
D) Is symmetric but only applicable for very large sample sizes
44. Which test is used to compare the means of two independent groups when the population standard deviation is unknown and sample sizes are small?
A) Z-test
B) Paired t-test
C) Independent samples t-test
D) Chi-square test
45. A z-test is appropriate when:
A) The population standard deviation is unknown and the sample size is small
B) The population standard deviation is known or the sample size is large (n > 30)
C) We are comparing variances of two independent groups
D) We are testing for independence in a contingency table
46. What is the critical value in hypothesis testing?
A) The observed test statistic from the sample
B) The maximum allowable probability of Type I error
C) The threshold value that separates the rejection region from the non-rejection region
D) The actual difference between sample means
47. The probability of rejecting a true null hypothesis is known as:
A) Type I Error (alpha)
B) Type II Error (beta)
C) Power of the test
D) Significance level
48. Which type of hypothesis states that there is no significant difference or relationship between variables?
A) Alternative Hypothesis (H1)
B) Research Hypothesis (RH)
C) Null Hypothesis (H0)
D) Composite Hypothesis
49. What is the primary purpose of hypothesis testing in statistics?
A) To estimate population parameters
B) To determine cause-and-effect relationships
C) To make decisions about population claims based on sample data
D) To summarize data using measures of central tendency
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