All Free Statistics MCQs with Answers

• A. the methods to make decisions about population based on sample results
• B. how to make decisions about mean, median, or mode
• C. how a sample is obtained from a population
• D. None of the above

Explanation: Inferential statistics uses sample results to draw conclusions or make decisions about the wider population.

• A. Mathematics
• B. Economics
• C. Statistic
• D. None of these

Explanation: A numerical measure calculated from a sample is called a statistic, such as the sample mean or sample proportion.

• A. Qualitative
• B. Ranked
• C. Both a and b
• D. None of these

Explanation: Non-parametric methods are suitable for qualitative data and for ordinal or ranked observations because they do not require the usual…

• A. Sign test
• B. Wilcoxon sign rank test
• C. Median test
• D. Kruskal Wallis test

Explanation: The Kruskal-Wallis test is the rank-based non-parametric counterpart of one-way ANOVA for comparing several independent groups.

• A. Parametric test
• B. Non parametric tests
• C. Either both
• D. None of these

Explanation: When the normality assumption is seriously violated, a non-parametric test is often preferred because it does not require a normal…

• A. Decrease
• B. Equal
• C. Increases
• D. None of these

Explanation: With the sample size and test design fixed, increasing alpha generally makes rejection easier, which increases power, 1-beta.

• A. Increase
• B. Decrease
• C. Yes
• D. No

Explanation: Alpha and beta are error probabilities under different hypotheses, so they are not complements in general.

• A. Kruskal Wallis Test
• B. Mann-Whitney U test
• C. Wilcoxon signed rank test
• D. Sign test

Explanation: The Mann-Whitney U test is the usual nonparametric alternative to the independent or unpaired two-sample t-test.

• A. Sign test
• B. None of these
• C. Runs test
• D. D Mann-Whitney U test

Explanation: The runs test examines whether the order of observations is random by comparing the observed number of runs with what randomness would…

• A. The Mann-Whitney test
• B. The Kruskal-Wallis test
• C. The Wilcoxon Signed Rank test
• D. The Kolmogorove-Simirnor test

Explanation: This is a goodness-of-fit question asking whether observed counts follow a specified binomial distribution.

• A. Any number of populations
• B. A sample mean to the population mean
• C. Two populations
• D. Three populations

Explanation: The Wilcoxon rank-sum test is the nonparametric alternative to the two-independent-samples t-test, so it compares two independent…

• A. Kolmogorov-Smirnor test
• B. Wilcoxon Rank-Sum test
• C. Spearman Rank Correlation test
• D. Kruskal-Wallis test

Explanation: The three firms provide three independent groups whose failure-time distributions or locations are being compared.

• A. There is an unusually large number of runs
• B. There is an unusually small number of runs
• C. None of these
• D. Either of the above

Explanation: Random sequences tend to produce a typical number of runs; both an unusually small number and an unusually large number indicate nonrandom…

• A. The Wilcoxon Rank-Sum test
• B. The Sign test
• C. None of the above
• D. Either of the above

Explanation: For two populations, the Wilcoxon rank-sum test can compare their locations using ranks, while the sign test can compare paired…

• A. 0.025
• B. 0.95
• C. 0.05
• D. Cannot be determined without more information

Explanation: Alpha is the Type I error probability, whereas beta is the Type II error probability and depends on the alternative value, sample size…

• A. Acceptance Region
• B. Type-I error
• C. Type-II Error
• D. Rejection Region

Explanation: If the significance level is α, the probability of not falling in the rejection region under the null hypothesis is 1 − α.

• A. β
• B. α
• C. (1 - α )
• D. (1 - β)

Explanation: Power is the probability of rejecting a false null hypothesis. Since β is the probability of a Type-II error, power equals 1 − β.

• A. Critical value
• B. Confidence limits
• C. Confidence boundaries
• D. None of these

Explanation: Critical values are the cutoff points that divide the rejection region from the non-rejection region.

• A. u = 20
• B. u ≠ 20
• C. u 20

Explanation: A simple hypothesis completely specifies one population parameter value, as in μ = 20.

• A. Among all other test of size α or less it has the largest power
• B. Among all other test of size α or greater it has the largest 1 - α
• C. Among all other test of size α or greater it has the smallest power
• D. Among all other test of size α or greater it has the largest β

Explanation: A most powerful test has the greatest power among all tests whose size is α or smaller.