statistical inference MCQs

Practise focused statistical inference questions with marked answers for exam preparation and subject revision.

statistical inference Mcqs
1. The critical value of a test statistic is determined from_____________?
comments icon0
A. The sampling distribution of the statistic assuming Alternative Hypothesis.

B. Non of these

C. The sampling distribution of the statistics assuming Null Hypothesis

D. calculations based on many actual repetitions of the same Experiment

2. The hypothesis which is being tested is called ___________________?
comments icon0
A. Null hypothesis

B. Composite hypothesis

C. Alternative hypothesis

D. Simple hypothesis

3. The non parametric equivalent of an unpaired samples t-test____________?
comments icon0
A. Mann-Whitney U test

B. Kruskal Wallis Test

C. Sign test

D. Wilcoxon signed rank test

4. For a biased estimator ? of ?, which one is correct_______________?
comments icon0

A. MSE(?)=Var(?)+Bias

B. MSE(?)=SD(?)+Bias

C. MSE(?)=Var(?)+Bias2

D. MSE(?)=SD(?)+Bias2

5. x=40 is estimator of _________________?
comments icon0

A. 6

B. Ux

C. 6/?n

D. (U)
6. Three brands of coffee are rated for tasted on a scale of 1 to 10. Six persons are asked to rate each brand so that there is a total of 18 observations.The appropriate test to tasted equally good is_____________?
comments icon0
A. Kruskal-Wallis test

B. Wilcoxon Rank-Sum test

C. Spearman Rank difference

D. One way analysis of variance (ANOVA)

7. A_______ is the specific value of the statistic used to estimate the population parameter?
comments icon0

A. None of these

B. Point estimator

C. Estimator

D. C.I.

8. E(x1 x2)= ___________________?
comments icon0

A. 6x x2

B. 62 x2

C. ux x2

D. u1 u2
9. If n = 400 and P=.69 then 90% C.I for P is _________________?
comments icon0

A. .798 and .745

B. .314 and .652

C. None of these

D. 652 and . 728
10. When testing for randomness, we can use_____________?
comments icon0

A. None of these

B. Runs test

C. D Mann-Whitney U test

D. Sign test

11. for two estimators T1=t1(X1,X2,.Xn) and T1=t1(X1,X2,.Xn) then estimators t1 is defined to be Rt1(?)?Rt2(?) for all ? in ? ?
comments icon0
A. Admissible estimator

B. Sufficient estimator

C. Minimax estimator

D. Consistent estimator

12. Which of the following test must be two-sided ?
comments icon0

A. Runs test

B. Sign test

C. Kruskal-Wallis

D. Wilcoxon Signed Rank

13. The minimum variance unbiased estimator of the population mean is _______________?
comments icon0

A. S/?n

B. 6x/?n

C. S2/n

D. 6/?n

14. To perform a Runs test for randomness the data must be_______________?
comments icon0

A. Divided into at least two classifications

B. Divided into exactly two classifications

C. Qualitative

D. Quantitative

15. For t distribution, increasing the sample size, the affect will be on ?
comments icon0

A. Standard Error of the Means

B. Degrees of Freedom

C. The t-ratio

D. All Above
16. An estimator Q is an unbiased estimator of the population parameter Q if ___________________?
comments icon0

A. E(Q) =Q

B. E(x) =

C. E(Q) =Q

D. E(P) = P

17. Comparing the times to failure of radar transponders made by firms A, B, and C based on an airlines sample experience with the three types of instruments one may use____________?
comments icon0
A. Kruskal-Wallis test

B. Spearman Rank Correlation test

C. Wilcoxon Rank-Sum test

D. Kolmogorov-Smirnor test

18. The Spearman Rank-Correlation test requires that the______________?
comments icon0

A. Data must be from two independent samples

B. Data must be measured on the same scale

C. Data should be of ordinal scale at least

D. Data must be distribution at least approximately as a t-distribution

19. The sign test assumes that the_______________?
comments icon0

A. The Wilcoxon Signed Rank test is used

B. Sample are dependent

C. Samples are independent

D. Samples have same mean

20. Power of test is denoted by _______________?
comments icon0

A. ?

B. (1 ?)

C. (1 ? )

D. ?

21. Analysis of Variance (ANOVA) is a test for equally of______________?
comments icon0

A. Proportions

B. Only two parameters

C. Means

D. Variances
22. If Ho is stated as Q = Qo< the alternate hypothesis in general stated________________?
comments icon0
A. Q ? Qo

B. None of these

C. Q Qo

23. ___________ is a value of sample statistics?
comments icon0

A. Probability

B. Numerical

C. Estimator

D. Estimate
24. The level of significance is denoted by _________________?
comments icon0

A. 1 ?

B. ?

C. ?

D. 1 ?

25. 1 ? is the probability of_____________?
comments icon0

A. Type-I error

B. Type-II Error

C. Acceptance Region

D. Rejection Region

26. Which of the following is simple hypothesis___________________?
comments icon0

A. u ? 20

B. u 20

C. u = 20
27. The Estimation and testing of hypothesis are main branches of ________________?
comments icon0

A. Regression

B. Probability distribution

C. Statistical Inference

D. Sampling

28. If E(?)=?, then ? is said to be_______________?
comments icon0
A. Unbiased

B. Consistent

C. Sufficient

D. Efficient

29. Herbicide A has been used for years in order to kill a particular type of weed. An experiment is to be conducted in order to see whether a new herbicide, Herbicide B, is more effective than Herbicide A. Herbicide A will continue to be used unless there is sufficient evidence that Herbicide B is more effective. The alternative hypothesis in this problem is_____________?
comments icon0

A. Herbicide A is not more effective than Herbicide B

B. Herbicide B is not more effective than Herbicide A

C. Herbicide A is more effective than Herbicide B

D. Herbicide B is more effective than Herbicide A

30. if Var(?)?0 as n ? 0, then ? is said to be______________?
comments icon0

A. Unbiased

B. Consistent

C. Efficient

D. Sufficient

31. Sample variance S2 is unbiased estimator of population variance 26 because ________________?
comments icon0

A. E(S2) = s2

B. E(u) = X

C. E(P) = P

D. Ux = u

32. The t distribution are_____________?
comments icon0

A. Same as Normal Curve

B. None of these

C. Skewed

D. Symmetrical
33. The Mann-Whitney U test is preferred to a t-test when____________?
comments icon0

A. Data are paired

B. Sample are dependent

C. Sample sizes are small

D. The assumption of normality is not met
34. if Var(T2)_______________?
comments icon0

A. Consistent

B. Sufficient

C. Unbiased

D. Efficient
35. Criteria to check a point estimator to be good are_____________?
comments icon0
A. All Above

B. Efficiency

C. Unbiasedness

D. Consistency

36. The Runs test results in rejecting the null hypothesis of randomness when______________?
comments icon0

A. None of these

B. Either of the above

C. There is an unusually small number of runs

D. There is an unusually large number of runs

37. Which of the following test is most likely assessing this null hypothesis: Ho The number of violations per apartment in the population of all city apartments is binomially distributed with a probability of success in any one trial of P=0.3 dd ?
comments icon0
A. The Kolmogorove-Simirnor test

B. The Kruskal-Wallis test

C. The Wilcoxon Signed Rank test

D. The Mann-Whitney test

38. The first and starting point in test Hypothesis is ______________?
comments icon0
A. stating Ho

B. stating H1

C. Test statistics

D. L of significance

39. Let X1,X2,Xn be a random sample from the density f(x;(?), where ? may be vector. If the conditional distribution of X1,X2,Xn given S=s does not depend on ? for any value of s of S, then statistic is called?
comments icon0

A. Minimax statistics

B. Minimal sufficient statistic

C. Efficient

D. Sufficient statistic

40. Parameter is a _________ quantity?
comments icon0
A. Constant

B. Non of these

C. All of above

D. Variable

41. if f(x1,x2,xn;?)=g(?;?)h(x1,x2,.,xn), then ? is____________?
comments icon0

A. Efficient

B. Unbiased

C. Sufficient

D. Consistent

42. Let X1,X2,,Xn be a random sample from a density,,,, f(x ? ?) where ? is a value of the random variable ?with known density g?(?) Then the estimator ?(?) with/ respect to the prior g?(?) is define as______________E[?(?)?X1,X2,..,Xn] is called?
comments icon0
A. Posterior Bays estimator

B. Sufficient estimator

C. Bays estimator

D. Minimax estimator

43. Let X1,X2,,Xn be a random sample from a density,,,, f(x ? ?) where ? is a value of the random variable ?with known density g?(?) Then the estimator ?(?) with/ respect to the prior g?(?) is define as_________________E[?(?)?X1,X2,..,Xn] is called?
comments icon0

A. Minimax estimator

B. Sufficient estimator

C. Posterior Bays estimator

D. Bays estimator

44. The values that separate the region of rejection and acceptance region are called _______________?
comments icon0

A. Confidence boundaries

B. None of these

C. Critical value

D. Confidence limits

45. When using the sign test, if two scores are tied, then_____________?
comments icon0

A. We count them

B. We depends upon the scores

C. We discard them

D. non of these

46. Consistency of an estimator can be checked by comparing____________?
comments icon0

A. mean Square Error

B. Mean

C. Variance

D. Standard Deviation

47. Which of the following is a true statement for comparing the t distribution with standard normal ?
comments icon0

A. The proportion of area beyond a specific value of t is less than the proportion of normal curve

B. Non of these

C. Greater the degree of freedom, the more the t-distribution resembles the standard normal distribution

D. The Normal Curve is symmetrical whereas the t-distribution are slightly skewed.

48. If we reject the null hypothesis, we might be making____________?
comments icon0
A. Type-II Error

B. Type-Error

C. A correct Decision

D. Unpredictable

49. In a Wilcoxon Rank-Sum test__________________?
comments icon0
A. Ties within one sample may affect the decision

B. Ties never affect the decision

C. Ties always affect the decision

D. Ties between the two sample may affect the decision

50. what is the probability of a type II error when ?=0.05 ?
comments icon0

A. 0.025

B. 0.05

C. 0.95

D. Cannot be determined without more information