Free Hypothesis Testing MCQs with Answers
24 Hypothesis Testing MCQs from Statistics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
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11. The Runs test results in rejecting the null hypothesis of randomness when______________?
- 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 ordering. Therefore, either extreme can lead to rejection of randomness.
Correct answer: Either of the above12. In testing for the difference between two populations, it is possible to use____________?
- 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 differences or a hypothesized median. Hence either test may be used, depending on the data structure and assumptions.
Correct answer: Either of the above13. what is the probability of a type II error when α=0.05 ?
- 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, variability, and test design. Therefore, alpha = 0.05 alone cannot determine beta.
Correct answer: Cannot be determined without more information14. 1 - α is the probability of_____________?
- 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. This is commonly called the acceptance or non-rejection region probability.
Correct answer: Acceptance Region15. Power of test is denoted by _______________?
- 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.
Correct answer: (1 - β)16. The values that separate the region of rejection and acceptance region are called _______________?
- 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 test statistic beyond the relevant cutoff leads to rejection of the null hypothesis.
Correct answer: Critical value17. Which of the following is simple hypothesis___________________?
- A. u = 20
- B. u ≠ 20
- C. u 20
Explanation: A simple hypothesis completely specifies one population parameter value, as in μ = 20. The alternatives μ ≠ 20 and an incomplete μ 20 do not specify one exact value.
Correct answer: u = 2018. A test is said to be most powerful test of size α, if_______________?
- 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. Restricting size prevents a test from appearing better merely by allowing a larger Type I error probability.
Correct answer: Among all other test of size α or less it has the largest power19. The first and starting point in test Hypothesis is ______________?
- A. stating H1
- B. stating Ho
- C. L of significance
- D. Test statistics
Explanation: Hypothesis testing begins by formulating the null hypothesis and the alternative hypothesis; among the choices, stating H₀ is the first step. Significance level and test statistic are selected or calculated afterward.
Correct answer: stating Ho20. If Ho is stated as Q = Qo< the alternate hypothesis in general stated________________?
- A. Q Qo
- B. Q ≠ Qo
- C. None of these
Explanation: When the null hypothesis specifies equality, H₀: Q = Q₀, the general two-sided alternative is H₁: Q ≠ Q₀. A one-sided alternative would require the question to state a direction such as greater than or less than.
Correct answer: Q ≠ Qo