Q.1 The Chi-square test is primarily used to test what?
Differences in means
Association between categorical variables
Variances of two populations
Trends in time series data
Explanation - The Chi-square test evaluates the independence or association between categorical variables in contingency tables.
Correct answer is: Association between categorical variables
Q.2 Which assumption is required for the Chi-square test?
Data must be normally distributed
Observations must be independent
Equal variances must exist
Sample size must be less than 30
Explanation - The Chi-square test assumes that each observation is independent of others in the dataset.
Correct answer is: Observations must be independent
Q.3 In a Chi-square test, expected frequency should generally be:
Greater than 1
At least 5
At least 10
Greater than 30
Explanation - Chi-square tests require expected frequencies of at least 5 in each cell for valid results.
Correct answer is: At least 5
Q.4 Which distribution does the Chi-square test statistic follow?
Normal distribution
T-distribution
Chi-square distribution
F-distribution
Explanation - The Chi-square test statistic follows the Chi-square distribution under the null hypothesis.
Correct answer is: Chi-square distribution
Q.5 Degrees of freedom in a Chi-square test of independence is calculated as:
(rows + columns)
(rows × columns)
(rows - 1) × (columns - 1)
(rows - 1) + (columns - 1)
Explanation - In Chi-square independence tests, degrees of freedom are calculated using (rows - 1) × (columns - 1).
Correct answer is: (rows - 1) × (columns - 1)
Q.6 Which type of data is required for a Chi-square test?
Nominal or categorical
Ordinal only
Interval
Ratio
Explanation - Chi-square test is designed for categorical or nominal data arranged in frequency tables.
Correct answer is: Nominal or categorical
Q.7 A low p-value in a Chi-square test suggests:
Strong evidence against null hypothesis
Support for the null hypothesis
Normality of data
Equal means
Explanation - A low p-value indicates significant association, hence rejecting the null hypothesis of independence.
Correct answer is: Strong evidence against null hypothesis
Q.8 Chi-square test is considered a:
Parametric test
Non-parametric test
Regression test
Correlation test
Explanation - The Chi-square test is non-parametric because it does not assume a specific population distribution.
Correct answer is: Non-parametric test
Q.9 Which test can be used as a non-parametric alternative to the t-test?
Wilcoxon signed-rank test
Chi-square test
Kolmogorov-Smirnov test
Runs test
Explanation - The Wilcoxon signed-rank test is a non-parametric alternative to the paired t-test.
Correct answer is: Wilcoxon signed-rank test
Q.10 When comparing two independent samples, the non-parametric equivalent of the t-test is:
Mann-Whitney U test
Chi-square test
Sign test
ANOVA
Explanation - The Mann-Whitney U test compares medians of two independent groups without assuming normality.
Correct answer is: Mann-Whitney U test
Q.11 The Kruskal-Wallis test is used instead of:
t-test
Chi-square test
ANOVA
Z-test
Explanation - Kruskal-Wallis test is a non-parametric alternative to ANOVA when assumptions of normality are violated.
Correct answer is: ANOVA
Q.12 Which test is used to assess the goodness of fit?
Chi-square test
Wilcoxon test
Runs test
Mann-Whitney U test
Explanation - The Chi-square goodness-of-fit test checks how well observed frequencies match expected frequencies.
Correct answer is: Chi-square test
Q.13 If Chi-square test statistic is very large, it implies:
High probability of null hypothesis
No relationship
Strong evidence against null hypothesis
Data is normally distributed
Explanation - A large Chi-square value means the observed data significantly deviates from expected frequencies.
Correct answer is: Strong evidence against null hypothesis
Q.14 Which of the following is NOT a non-parametric test?
Mann-Whitney U
Kruskal-Wallis
ANOVA
Wilcoxon signed-rank
Explanation - ANOVA is a parametric test, unlike the others listed which are non-parametric.
Correct answer is: ANOVA
Q.15 The sign test is used for:
Testing correlation
Testing median differences
Testing means
Testing variance
Explanation - The sign test is a simple non-parametric test for comparing medians in paired data.
Correct answer is: Testing median differences
Q.16 Kolmogorov-Smirnov test is used to test:
Equality of variances
Normality of distribution
Independence of variables
Association of categorical data
Explanation - The Kolmogorov-Smirnov test checks whether data follows a specified distribution, often normality.
Correct answer is: Normality of distribution
Q.17 Which test is most appropriate for paired non-parametric data?
Chi-square test
Wilcoxon signed-rank test
Kruskal-Wallis test
Runs test
Explanation - The Wilcoxon signed-rank test is used for paired data where parametric assumptions do not hold.
Correct answer is: Wilcoxon signed-rank test
Q.18 In Chi-square tests, what happens if expected frequencies are too low?
Test becomes invalid
P-value becomes smaller
Degrees of freedom reduce
Results remain unaffected
Explanation - Low expected frequencies violate Chi-square assumptions and make the test unreliable.
Correct answer is: Test becomes invalid
Q.19 Non-parametric tests are generally used when:
Data is normally distributed
Sample size is large
Data is ordinal or nominal
Variance is homogeneous
Explanation - Non-parametric tests are suitable for ordinal, nominal, or non-normally distributed data.
Correct answer is: Data is ordinal or nominal
Q.20 Which non-parametric test can be used for more than two related samples?
Sign test
Friedman test
Chi-square test
Kruskal-Wallis test
Explanation - The Friedman test is the non-parametric equivalent of repeated-measures ANOVA.
Correct answer is: Friedman test
Q.21 A researcher wants to check if dice are fair. Which test should be applied?
ANOVA
Chi-square goodness-of-fit test
Sign test
Wilcoxon test
Explanation - The Chi-square goodness-of-fit test compares observed dice outcomes with expected probabilities.
Correct answer is: Chi-square goodness-of-fit test
Q.22 The Mann-Whitney U test compares:
Means of two groups
Variances of two groups
Medians of two groups
Frequencies of categories
Explanation - Mann-Whitney U test compares medians and ranks between two independent samples.
Correct answer is: Medians of two groups
Q.23 Which of the following is an assumption of non-parametric tests?
Normality
Independence of observations
Equal variances
Large sample size
Explanation - Non-parametric tests relax distribution assumptions but still require independent observations.
Correct answer is: Independence of observations
Q.24 Chi-square test cannot be used when:
Data is categorical
Frequencies are low
Sample size is large
Degrees of freedom are high
Explanation - Chi-square test loses reliability when expected frequencies in cells are too low.
Correct answer is: Frequencies are low
Q.25 Which test is used to check randomness in data?
Runs test
Wilcoxon signed-rank test
Kruskal-Wallis test
Chi-square test
Explanation - The Runs test checks whether a sequence of data points occurs in a random order.
Correct answer is: Runs test