All Free Statistics MCQs with Answers
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545 questions · page 30 of 55
291. The Wilcoxon, Rank-Sum test used to compares_______________?
- 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 populations. It is not designed for three or more populations; Kruskal-Wallis is used for that setting.
Correct answer: Two populations292. Comparing the times to failure of radar transponders made by firms A, B, and C based on an airline's sample experience with the three types of instruments one may use____________?
- 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. Kruskal-Wallis extends the rank-sum approach from two groups to three or more, so it is the appropriate choice.
Correct answer: Kruskal-Wallis test293. 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 above294. 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 above295. 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 information296. 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 Region297. 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)298. 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 value299. 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 = 20300. 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 power