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#### New Statistical Interference( Statistics ) MCQs – Up To Date Statistics MCQs

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#### Latest Statistics MCQs

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**Statistical Interference( Statistics )****Let X1,X2,……,Xn be a random sample from a density,,,, f(x ι θ) where θ is a value of the random variable Θwith known density gΘ(θ) Then the estimator ∏(θ) with…/ respect to the prior gΘ(θ) is define as______________E[∏(θ)ιX1,X2,…..,Xn] is called?**

**A. Posterior Bay’s estimator**

B. Bay’s estimator

C. Minimax estimator

D. Sufficient estimator

**The non parametric equivalent of an unpaired samples t-test____________?**

A. Wilcoxon signed rank test**B. Mann-Whitney U test**

C. Kruskal Wallis Test

D. Sign test

**When testing for randomness, we can use_____________?**

A. None of these

B. Sign test**C. Runs test**

D. D Mann-Whitney U test

**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 ?**

A. The Kruskal-Wallis test

B. The Mann-Whitney test

C. The Wilcoxon Signed Rank test**D. The Kolmogorove-Simirnor test**

**Which of the following test must be two-sided ?**

**A. Sign test**

B. Kruskal-Wallis

C. Wilcoxon Signed Rank

D. Runs test

**The Wilcoxon, Rank-Sum test used to compares_______________?**

A. A sample mean to the population mean

B. Any number of populations**C. Two populations**

D. Three populations

**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. Wilcoxon Rank-Sum test

B. Kolmogorov-Smirnor test

C. Spearman Rank Correlation test**D. Kruskal-Wallis test**

**In testing for the difference between two populations, it is possible to use____________?**

A. The Sign test

B. The Wilcoxon Rank-Sum test

C. None of the above**D. Either of the above**

**The Runs test results in rejecting the null hypothesis of randomness when______________?**

A. There is an unusually small number of runs

B. There is an unusually large number of runs

C. None of these**D. Either of the above**

**The critical value of a test statistic is determined from_____________?**

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

B. The sampling distribution of the statistics assuming Null Hypothesis**C. The sampling distribution of the statistic assuming Alternative Hypothesis.**

D. Non of these

**what is the probability of a type II error when α=0.05 ?**

A. 0.05

B. 0.95

C. 0.025**D. Cannot be determined without more information**

**condition for applying Central Limit Theorem (CLT) which approximate the sampling distribution of the mean with a normal distribution is ?**

**A. n > 30**

B. 2 n 5

C. N(1 – p) > 5

E. N < 30

**For t distribution, increasing the sample size, the affect will be on ?**

A. The t-ratio

B. Standard Error of the Means

C. Degrees of Freedom**D. All Above**

**A quantity obtained by applying certain rule or formula is known as ________________?**

**A. Estimate**

B. Estimation

C. Test Statistics

D. Sample

E. Estimator

**Analysis of Variance (ANOVA) is a test for equally of______________?**

**A. Variances**

B. Means

C. Only two parameters

D. Proportions

**If we reject the null hypothesis, we might be making____________?**

A. A correct Decision

B. Unpredictable**C. Type-II Error**

D. Type-Error

**Parameter is a _________ quantity?**

**A. Constant**

B. Variable

C. All of above

D. None of above

**1 – α is the probability of_____________?**

**A. Acceptance Region**

B. Type-II Error

C. Type-I error

D. Rejection Region

**Power of test is denoted by _______________?**

A. α

B. β

C. (1 – α )**D. (1 – β)**

**The values that separate the region of rejection and acceptance region are called _______________?**

**A. Critical value**

B. Confidence boundaries

C. Confidence limits

D. None of these

#### Sample Linear Regression MCQs

**The level of significance is denoted by _________________?**

A. β

B. 1 – ∞**C. ∞**

D. 1 – β

**If n = 400 and P=.69 then 90% C.I for P is _________________?**

**A. 652 and . 728**

B. .798 and .745

C. .314 and .652

D. None of these

**Which of the following is simple hypothesis___________________?**

**A. u = 20**

B. u 20

C. u ≠ 20

D. u 30

**E(x1 – x2)= ___________________?**

A. 6x – x2**B. u1 – u2**

C. ux – x2

D. 6×2 – x2

**95% confidence limits u are ________________?**

A. u±1.95 S/√n

B. x±1.65 6/√n**C. x±1.96 6/√n**

D. ±1.96 6/√n

**The minimum variance unbiased estimator of the population mean is _______________?**

A. S/√n

B. 6/√n**C. S2/n**

D. 6x/√n

**__________ is the process of using sample information to reach?**

A. Biased

B. Population**C. Unbiased**

D. Increase

**_________ is an estimate expressed by a single value?**

A. Point estimator

B. C.I.

C. Parameter**D. Point estimate**

**x=40 is estimator of _________________?**

**A. (U)**

B. Ux

C. 6

D. 6/√n

**Sample variance S2 is unbiased estimator of population variance 26 because ________________?**

A. E(u) = X

B. E(S2) = s2**C. E(P) = P**

D. Ux = u

**Sample proportion P is __________ estimator?**

A. Parameter

B. Biased**C. Unbiased**

D. None of these

**An estimator Q is an unbiased estimator of the population parameter Q if ___________________?**

A. E(Q) =Q**B. E(Q) =Q**

C. E(x) = µ

D. E(P) = P

**Let X1,X2,……,Xn be a random sample from a density,,,, f(x ι θ) where θ is a value of the random variable Θwith known density gΘ(θ) Then the estimator ∏(θ) with…/ respect to the prior gΘ(θ) is define as_________________E[∏(θ)ιX1,X2,…..,Xn] is called?**

**A. Posterior Bay’s estimator**

B. Bay’s estimator

C. Minimax estimator

D. Sufficient estimator

**If E(θˆ)=θ, then θˆ is said to be_______________?**

**A. Unbiased**

B. Sufficient

C. Consistent

D. Efficient

**if Var(T2)_______________?**

**A. Efficient**

B. Unbiased

C. Sufficient

D. Consistent

**for two estimators T1=t1(X1,X2,….Xn) and T1=t1(X1,X2,….Xn) then estimators t1 is defined to be Rt1(θ)≤Rt2(θ) for all θ in Θ ?**

A. Sufficient estimator**B. Admissible estimator**

C. Consistent estimator

D. Minimax estimator

**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 β

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 1 – α

**If the conditional distribution of X1,X2,…..Xn given S=s, does not depends on θ, for any value of S=s the statistics S=s(X1,X2,…..Xn) is called______________?**

A. Consistent**B. Sufficient**

C. Unbiased

D. Efficient

#### Probability MCQs

**A set of jointly sufficient statistic is defined to be minimal sufficient if and only if_______________?**

A. It is a function of any sufficient statistics in the set.**B. It is a function of every other set of sufficient**

C. It is a function of some other set of sufficient statistics.

D. It is not a function of every other set of sufficient statistics.

**For a biased estimator θˆ of θ, which one is correct_______________?**

A. MSE(θˆ)=SD(θˆ)+Bias2**B. MSE(θˆ)=Var(θˆ)+Bias2**

C. MSE(θˆ)=SD(θˆ)+Bias

D. MSE(θˆ)=Var(θˆ)+Bias

**Let Z1,Z2,….Zn be independent and identically distributedrandom variable, satisfying E[ι Zt ι]<∞. Let N be an integer valued random variable whose value n depends only on the values of the first n Z¡’s. Suppose E(N)< ∞, then E(Z1,Z2,….Zn)=E(N)E(Z) is called ?**

**A. Independence Equation**

B. Neyman Pearson Lemma

C. Sequential Probability Likelihood Equation

D. Wald’s Equation

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

**A. Minimal sufficient statistic**

B. Efficient

C. Sufficient statistic

D. Minimax statistics

**if Var(θˆ)→0 as n → 0, then θˆ is said to be______________?**

A. Efficient

B. Sufficient

C. Unbiased**D. Consistent**

**if f(x1,x2,…xn;θ)=g(θˆ;θ)h(x1,x2,….,xn), then θˆ is____________?**

A. Efficient**B. Sufficient**

C. Consistent

D. Unbiased

**Which of the following test use Rank Sums____________?**

**A. Kruskal-Wallis and Wilcoxon tests**

B. Chi-Square and sign test

C. Runs test

D. F test

**Wilcoxon Rank-Sum test can be of_______________?**

A. Upper tailed

B. Lower tailed**C. Either of the above**

D. None of the above

**When using the sign test, if two scores are tied, then_____________?**

A. We depends upon the scores**B. We discard them**

C. We count them

D. none of these

**In a Wilcoxon Rank-Sum test__________________?**

**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

**The Spearman Rank-Correlation test requires that the______________?**

A. Data must be from two independent samples**B. Data should be of ordinal scale at least**

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

D. Data must be measured on the same scale

**To perform a Runs test for randomness the data must be_______________?**

A. Quantitative**B. Divided into exactly two classifications**

C. Divided into at least two classifications

D. Qualitative

**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_____________?**

A. One way analysis of variance (ANOVA)

B. Wilcoxon Rank-Sum test

C. Spearman Rank difference**D. Kruskal-Wallis test**

**The sign test assumes that the_______________?**

A. Samples have same mean

B. Samples are independent**C. Sample are dependent**

D. The Wilcoxon Signed Rank test is used

**The Mann-Whitney U test is preferred to a t-test when____________?**

A. Sample sizes are small**B. The assumption of normality is not met**

C. Sample are dependent

D. Data are paired

**Which of the following is a true statement for comparing the t distribution with standard normal ?**

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

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

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

D. Non of these

**The t distribution are_____________?**

**A. Symmetrical**

B. Skewed

C. Same as Normal Curve

D. None of these

**Which of the following is an assumption underlying the use of the t-distribution ?**

**A. The sample are drawn from a normally distributed population.**

B. The variance of the population is known

C. s (sample standard deviation) is an unbiased estimate of the population variance.

D. All above

#### Presentation Of Data MCQs

**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_____________?**

A. Herbicide A is not more effective than Herbicide B

B. Herbicide A is more effective than Herbicide B

C. Herbicide B is more effective than Herbicide A**D. Herbicide B is not more effective than Herbicide A**

**Consistency of an estimator can be checked by comparing____________?**

A. Mean

B. Standard Deviation

C. mean Square Error**D. Variance**

**Criteria to check a point estimator to be good are_____________?**

A. Unbiasedness**B. All Above**

C. Consistency

D. Efficiency

**The first and starting point in test Hypothesis is ______________?**

A. L of significance**B. stating Ho**

C. stating H1

D. Test statistics

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

A. Q Qo**B. Q ≠ Qo**

C. All of these

D. None of these

**Which of the following cannot be Ho_________________?**

A. Q ≥ Qo

B. Q ≤ Qo

C. Q = Qo**D. Q ≠ Qo**

**Type II error is committed when the null hypothesis is _________________?**

A. Accepted when it is true

B. Rejected when it is false

C. Rejected when it is true**D. Accepted when it is false**

**The hypothesis which is being tested is called ___________________?**

A. Alternative hypothesis

B. Composite hypothesis**C. Null hypothesis**

D. Simple hypothesis

**95% confidence limits for P are _________________?**

A. P±1.65(pq/n)

B. P±2.18√p2q2/n

C. P±1.96 p2q2/√n**D. P±1.96√p2q2/n**

**The Estimation and testing of hypothesis are main branches of ________________?**

A. Probability distribution

B. Sampling

C. Regression**D. Statistical Inference**

**___________ is a value of sample statistics?**

**A. Estimate**

B. Probability

C. Estimator

D. Numerical

**Sampling Error decrease by _______ the sample size?**

A. Decrease

B. Increase

C. Sampling**D. Population**

**Since E(X) _______X is said to be unbiased estimator of the population mean?**

A. X

B. Q

C. Ux**D. u**

**A_______ is the specific value of the statistic used to estimate the population parameter?**

**A. Point estimator**

B. Estimator

C. C.I.

D. None of these