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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_____________?
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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 ___________________?
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A. Null hypothesis

B. Composite hypothesis

C. Alternative hypothesis

D. Simple hypothesis

3. The non parametric equivalent of an unpaired samples t-test____________?
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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_______________?
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A. MSE(?)=Var(?)+Bias

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

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

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

5. x=40 is estimator of _________________?
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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_____________?
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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?
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A. None of these

B. Point estimator

C. Estimator

D. C.I.

8. E(x1 x2)= ___________________?
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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 _________________?
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A. .798 and .745

B. .314 and .652

C. None of these

D. 652 and . 728

10. When testing for randomness, we can use_____________?
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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 ? ?
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A. Admissible estimator

B. Sufficient estimator

C. Minimax estimator

D. Consistent estimator

12. Which of the following test must be two-sided ?
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A. Runs test

B. Sign test

C. Kruskal-Wallis

D. Wilcoxon Signed Rank

13. The minimum variance unbiased estimator of the population mean is _______________?
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A. S/?n

B. 6x/?n

C. S2/n

D. 6/?n

14. To perform a Runs test for randomness the data must be_______________?
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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 ?
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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 ___________________?
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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____________?
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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______________?
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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_______________?
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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 _______________?
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A. ?

B. (1 ?)

C. (1 ? )

D. ?

21. Analysis of Variance (ANOVA) is a test for equally of______________?
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A. Proportions

B. Only two parameters

C. Means

D. Variances

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

B. None of these

C. Q Qo

23. ___________ is a value of sample statistics?
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A. Probability

B. Numerical

C. Estimator

D. Estimate

24. The level of significance is denoted by _________________?
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A. 1 ?

B. ?

C. ?

D. 1 ?

25. 1 ? is the probability of_____________?
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A. Type-I error

B. Type-II Error

C. Acceptance Region

D. Rejection Region

26. Which of the following is simple hypothesis___________________?
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A. u ? 20

B. u 20

C. u = 20

27. The Estimation and testing of hypothesis are main branches of ________________?
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A. Regression

B. Probability distribution

C. Statistical Inference

D. Sampling

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

B. Consistent

C. Efficient

D. Sufficient

31. Sample variance S2 is unbiased estimator of population variance 26 because ________________?
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A. E(S2) = s2

B. E(u) = X

C. E(P) = P

D. Ux = u

32. The t distribution are_____________?
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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____________?
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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)_______________?
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A. Consistent

B. Sufficient

C. Unbiased

D. Efficient

35. Criteria to check a point estimator to be good are_____________?
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A. All Above

B. Efficiency

C. Unbiasedness

D. Consistency

36. The Runs test results in rejecting the null hypothesis of randomness when______________?
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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 ?
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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 ______________?
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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?
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A. Minimax statistics

B. Minimal sufficient statistic

C. Efficient

D. Sufficient statistic

40. Parameter is a _________ quantity?
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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____________?
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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?
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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?
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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 _______________?
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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_____________?
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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____________?
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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 ?
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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____________?
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A. Type-II Error

B. Type-Error

C. A correct Decision

D. Unpredictable

49. In a Wilcoxon Rank-Sum test__________________?
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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 ?
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A. 0.025

B. 0.05

C. 0.95

D. Cannot be determined without more information

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