Nonparametric Tests Multiple Choice Questions and answers (mcqs)

 1- Nonparametric Tests referred to as _ : ?

(A) Distribution-free test      (B) Z-test

Option (A) is correct.

2- We always use _ when the mean more accurately the center of distribution of your data and sample size is large enough: ?

(A) Parametric Test             (B) Nonparametric Test

Option (A) is correct.

3- If the Median more accurately represents the center of distribution of your data, use a _ even If you have a large size: ?

(A) Nonparametric Test      (B) Parametric Test

Option (A) is correct.

4- Chi-Square test is a _ : ?

(A) Parametric Statistic      (B) Nonparametric Statistic

Option (B) is correct.

5- T-Tests or Z-Tests are a type of _ method: ?

(A) Parametric                    (B) Nonparametric

Option (A) is correct.

6- The nonparametric tests may be applied to _ data or data that can be ranked but not measured exactly: ?

(A) Quantitative                 (B) Qualitative

Option (B) is correct.

7- Nonparametric Tests are generally _ : ?

(A) Less Efficient              (B) More Efficient

Option (A) is correct.

8- Nonparametric tests require a _ sample size than do the corresponding parametric tests: ?

(A) Larger                         (B) Smaller

Option (A) is correct.

9- Sign test is used to test the _ : ?

(A) Alternative Hypothesis   (B) Null Hypothesis

Option (B) is correct.

10- Analysis of Variance (ANOVA) is: ?

(A) Parametric                      (B) Nonparametric

Option (A) is correct.

11- Rank Correlation is: ?

(A) Nonparametric              (B) Parametric

Option (A) is correct.

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Statistical Inference in Regression and Correlation Multiple Choice Questions and answers (mcqs)

 1- Fisher's z-transformation is denoted as: ?

(A) Zf                                 (B) F

Option (A) is correct.

2- The Process of analysing the total variation in the dependent variable Y into its components; one explained by regression line and the other residual or unexplained part is defined as: ?

(A) Analysis of Variance for Regression (B) ANCOVA

Option (A) is correct.

3- Total SS(Sum of Squares) =: ?

(A) Within SS + Between SS   (B) Residual or Error SS(SSE) + Regression SS(SSR)

Option (B) is correct.

4- In ANOVA for Multiple Regression and Testing Hypothesis about the "beta" parameters, degrees of freedom are: ?

(A) V1 = 2, V2 = n - 3            (B) V1 = k - 1, V2= n - k

Option (A) is correct.

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Experimental Designs Multiple Choice Questions and answers (mcqs)

 1- Experimental Design means _ used to collect the data: ?

(A) Plan                                (B) Designing

Option (A) is correct.

2- The Purpose of randomization is to _ bias and other sources of extraneous variation: ?

(A) Accept                             (B) Remove

Option (B) is correct.

3- A term reffering  to the amount of balancing, blocking and grouping of the experimental units is called as: ?

(A) Local Control                  (B) Replication

Option (A) is correct.

4- A Completely Randomized Design (CR) design is also called as: ?

(A) One-Way ANOVA           (B) Two-way ANOVA

Option (A) is correct.

5- A Randomized Complete Block Design (RCB) is also defined as: ?

(A) Two-Way ANOVA           (B) One-Way ANOVA

Option (A) is correct.

6- A Replication is used to secure more accurate estimate of the _ : ?

(A) Repetition                        (B) Experimental Error

Option (B) is correct.

7- A Replication is used to _ the experimental error and thereby to increase precision: ?

(A) Increase                            (B) Decrease

Option (B) is correct.

8- A Completely Randomized (CR) design is one in which treatments are assigned to experimental units completely _ : ?

(A) At Random                       (B) At Most

Option (A) is correct.

9- In CR Design, There is possibility of entering the whole of the variation among the experimental units into the _ as the randomization is not restricted in any direction: ?

(A) experimental error            (B) Design 

Option (A) is correct.

10- Complete Randomized Block (RCB) Design controls variability only in: ?

(A) 3 direction                        (B) 1 direction

Option (B) is correct.

11- Latin Square (LS) Design is also called as: ?

(A) Two-way ANOVA            (B) Three-way ANOVA

Option (B) is correct.

12- In Latin Square (LS) Design, treatments are grouped in blocks in: ?

(A) Two directions                  (B) One direction

Option (A) is correct.

13- In Latin Square Design, Rows, Columns and Treatments are always: ?

(A) Not Equal                          (B) Equal

Option (B) is correct.

14- In Latin Square (LS) Design , the degree of freedom, V2 is the: ?

(A) Error Degree of Freedom   (B) Nothing

Option (A) is correct.

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Analysis of Covariance (ANCOVA) Multiple Choice Questions and answers (mcqs)

 1- Analysis of Covariance is abbreviated as: ?

(A) ANCOVA                        (B) ANOVA

Option (A) is correct.

Note: But, ANOVA shows here Analysis of Variance.

2- ANCOVA is a blending of ANOVA and _: ?

(A) Regression                       (B) Correlation

Option (A) is correct.

3- Control Variables are called as: ?

(A) Correlated                        (B) Covariates

Option (B) is correct.

4- ANCOVA has a _ Continuous Response Variable: ?

(A) Double                             (B) Single

Option (B) is correct.

5- Concomitant Variable or Covariate is denoted as: ?

(A) X                                       (B) Y

Option (A) is correct.

6- In ANCOVA, the Populations are Normally distributed with _ Variances: ?

(A) Homogeneous                   (B) Heterogeneous

Option (A) is correct.

7- The Covariance adjustments remove the _ due to regression: ?

(A) Covariates                         (B) Bias

Option (B) is correct.

8- In ANCOVA, the regression is _ and the slope is not _ : ?

(A) Quadratic, 1                       (B) Linear, Zero

Option (B) is correct.

9- In ANCOVA, Treatment, Block and Regression effects are _ : ?

(A) Additive                              (B) Multiplicative

Option (A) is correct.

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Analysis of Variance (ANOVA) Multiple Choice Questions and answers (mcqs)

 1- The Analysis of Variance is abbreviated as: ?

(A) ANOVA                         (B) ANCOVA

Option (A) is correct.

2- Analysis of Variance is introduced by: ?

(A) Sir R.A. Fisher              (B) G.W Snedecor

Option (A) is correct.

3- For Testing more than two Means, we always use: ?

(A) t-distribution                  (B) Analysis of Variance(ANOVA)

Option (B) is correct.

4- In One-way ANOVA, Total SS(Sum of Squares) =: ?

(A) SSR + SSC + SSE         (B) Within SS + Between SS

Option (B) is correct.

5- Within SS(Sum of Squares) is also called as: ?

(A) Error SS                         (B) Between SS

Option (A) is correct.

6- In Analysis of Variance , the more the sample means differ the _ the variance becomes: ?

(A) Smaller                           (B) Larger

Option (B) is correct.

7- The Analysis of Variance compares two different estimates of variance by using F-distribution to determine whether the Population Means are: ?

(A) Equal                               (B) Not Equal

Option (A) is correct.

Note; Must remember that  in Null Hypothesis " Ho : All means are equal".

8- In One-way ANOVA, Columns "c" is also equal to: ?

(A) k                                      (B) f

Option (A) is correct.

9- In One-way ANOVA, degrees of freedom are: ?

(A) V1 = k - 1  ,  V2 = n - k       (B) V1 = r - 1,   V2 = (r - 1)(c - 1)

Option (A) is correct.

Note: But, In Two-way ANOVA, degrees of freedom are V1 = r - 1, V2 = (r - 1)(c - 1) & also V1 = c - 1,   V2= (r - 1)(c - 1).

10- In Two-way ANOVA, Total SS (SST) =: ?

(A) SSR + SSC + SSE                (B) Within SS + Between SS

Option (A) is correct.

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F-Distribution Multiple Choice Questions and answers (mcqs)

 1- Two normally distributed populations having Equal Variances is defined as: ?

(A) F-Distribution                      (B) Z-Distribution

Option (A) is correct.

2- F-Distribution has shape as same as the shape of: ?

(A) Chi-Square                          (B) Normal 

Option (A) is correct.

3- The Range of F-Distribution is from: ?

(A) - infinity to + infinity          (B) 0 to infinity

Option (B) is correct.

Note: Chi-Square also have a Range from '0 to infinity'.

4- F-Distribution has _ skewness: ?

(A) Negative                             (B) Positive

Option (B) is correct.

Note: Must remember that Chi-Square also have a Positive Skewness.

5- F-Distribution approaches Normal Distribution when V1 and V2 (degrees of freedom) becomes: ?

(A) larger                                 (B) Smaller

Option (A) is correct.

6- 1/F has a an F-Distribution with Degrees of Freedom: ?

(A) V1 and V2                         (B) V2 and V1

Option (B) is correct.

7- If V1 = V2, then 1/F is same as that of: ?

(A) F                                        (B) 1/F

Option (A) is correct.

8- The Mean of the F-Distribution with V1 and V2 degrees of freedom are: ?

(A) V2/V2 - 2  for V2 > 2        (B) V2/V1

Option (A) is correct.

9- F-distribution can be applied If the two samples are _ and randomly selected: ?

(A) Dependently                      (B) Independently

Option (B) is correct.

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Student's t-distribution Multiple Choice Questions and answers (mcqs)

 1- In Student's t-distribution, Degree of Freedom "v" =: ?

(A) n - 1                       (B) m - 1

Option (A) is correct.

2- The shape of t-distribution is: ?

(A) Bell Shaped         (B) Square Shaped

Option (A) is correct.

Note: Must remember that also the shape of Normal Distribution "Z" is bell shaped.

3- t-distribution has range from: ?

(A) 0 to infinity         (B) - infinity to + infinity

Option (B) is correct.

Note: Also Normal Distribution 'Z' has range from " - infinity to + infinity ".

4- t-distribution has shape as same as the shape of: ?

(A) Chi-Square         (B) Normal Distribution

Option (B) is correct.

5- The Variance of t-distribution is: ?

(A) v/v - 2                (B) v/2

Option (A) is correct.

6- t-distribution approaches to the normal distribution as 'V' or size 'n' becomes: ?

(A) Larger               (B) Smaller

Option (A) is correct.

7- The Mean of the t-distribution is Zero, when: ?

(A) v < 2                 (B) v > 2

Option (B) is correct.

Note: The Mean is undefined for v = 1.

8- 'SP' of Student's t-distribution have_ formulae: ?

(A) three                 (B) four

Option (A) is correct.

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Chi Square Distribution Multiple Choice Questions and answers (mcqs)

 1- Chi-Square Distribution has Range from: ?

(A) - infinity to + infinity    (B) 0 to infinity

Option (B) is correct.

2- The Curve of a Chi-Square Distribution is _ Skewed: ?

(A) Positively         (B) Negatively

Option (A) is correct.

3- Chi-Square Distribution tends to Normal Distribution as the number of degree of freedom approaches: ?

(A) Infinity             (B) Zero

Option (A) is correct.

4- In Test of Independence, alpha means: ?

(A) not B                 (B) not A

Option (B) is correct.

5- Attribute is also called as: ?

(A) Qualitative Variable  (B) Quantitative Variable

Option (A) is correct.

6- If Co-efficient of Association, Q=1, then Attributes are: ?

(A) Disassociated            (B) Completely Associated

Option (B) is correct.

7- The Range of Co-efficient of Association lies between: ?

(A) - 1 and + 1                (B) 0 to infinity

Option (A) is correct.

8- Associated means: ?

(A) Independent             (B) Not Independent

Option (B) is correct.

9- If (AB) = (A) (B)/n, then Attributes A and B are called as: ?

(A) Associated               (B) Independent

Option (B) is correct.

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Hypothesis Testing Multiple Choice Questions and answers (mcqs)

 1- Type - I Error is made by Rejecting of Ho If Ho is: ?

(A) True                   (B) False

Option (A) is correct.

Note: But, must remember that Type - II Error is made by Accepting of Ho If Ho is False.

2- Which of the following is not the Simple Hypothesis: ?

(A) Ho : Mean = 60        (B) H1 : Mean > 60

Option (B) is correct.

Note: Simple Hypothesis is One in which all the parameters of the distribution are specified. For Example, Ho: Mean=60.

3- Rejection Region is also called as: ?

(A) Critical Value            (B) Critical Region

Option (B) is correct.

4- Power of Test =: ?

(A) 1 - alpha             (B) 1 - betta

Option (B) is correct.

5- Level of Significance is denoted as: ?

(A) alpha                   (B) betta

Option (A) is correct.

6- Most Common Values of alpha are: ?

(A) 5 %  or 1 %        (B) 2 % or 3 %

Option (A) is correct.

7- Test-statistic is a: ?

(A) Value                  (B) Formula

Option (B) is  correct.

Note: Test-statistic is a sample statistic or formula which provides a basis for testing the null hypothesis.

8- If Ho is Rejected after testing is called as: ?

(A) Insignificant Testing    (B) Significant Testing

Option (B) is correct.

Note: But, If Ho is Accepted after testing is called as Insignificant Testing.

9- Type - I Error is denoted by: ?

(A) alpha            (B) betta

Option (A) is correct.

Note: But, Type - II Error is denoted as 'betta'.

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Statistical Inference Multiple Choice Questions and answers (mcqs)

 1- Discussion about Population Parameter on the basis of Sample Observations is called as: ?

(A) Statistical Inference       (B) Inferential Statistics 

Option (A) is correct.

2- The Estimator is defined as: ?

(A) Formula             (B) Value

Option (A) is correct.

Note: But, Estimate is a Value.

3- An Estimator would be Consistent If Variance of this Estimator becomes _  as n approaches infinity: ?

(A) Nine                  (B) Zero

Option (B) is correct.

4- If Efficiency > 1, then T is _ efficient: ?

(A) More                 (B) Less

Option (A) is correct.

5- T1 will be more efficient than T2 If: ?

(A) Var (T1) > Var(T2)     (B) Var(T1) < Var(T2)

Option (B) is correct.

6- BLUE is abbreviated as: ?

(A) Best Linear Unbiased Estimator   (B) Blue Light Union Enter

Option (A) is correct.

7- In BLUE, Variance is always: ?

(A) Least                (B) at most

Option (A) is correct.

8- Level of Confidence is: ?

(A) alpha                (B) 1 - alpha

Option (B) is correct.

9- Confidence Coefficient is always: ?

(A) ( 1 - alpha ) 100 %   (B) 1 - alpha

Option (A) is correct.

10- Is an Estimator a Random Variable: ?

(A) No                     (B) Yes

Option (B) is correct.

Note: Yes, Estimator is a random variable because Estimator has different Probability Distributions.

11- For Checking the Unbiasedness of Estimators T1 and T2, we should take: ?

(A) Expectation         (B) Variance

Option (A) is correct.

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Survey Sampling and Sampling Distributions Multiple Choice Questions and answers (mcqs)

 1- Sample is a part of: ?

(A) Population      (B) Proportion

Option (A) is correct.

2- If n < 5% of N, then we always use: ?

(A) With Replacement (B) Without Replacement 

Option (A) is correct.

Note: If n > 5% of N, then we always use Without Replacement.

3- Sample Proportion 'p' =: ?

(A) X/N                 (B) x/n

Option (B) is correct.

Note : Must remember that Population Proportion 'P' = X/N.

4- Sample Mean is also called: ?

(A) Combined Mean  (B) Geometric Mean

Option (A) is correct.

5- Sampling Error is reduced , when Sample Size 'n': ?

(A) Decreases          (B) Increases

Option (B) is correct.

6- The Systematic Component of error which deprives a survey result of representativeness is defined as: ?

(A) Bias           (B) Sampling Bias

Option (A) is correct.

7- Quota Sample is a Type of: ?

(A) Judgement Sample (B) Sampling Error

Option (A) is correct.

8- Finite Population Correction Factor is: ?

(A) N/n            (B) N-n/N-1

Option (B) is correct.

9- Non-Sampling Errors are: ?

(A) Human Errors   (B) Bias

Option (A) is correct.

10- Method to select suitable sample from population is called as: ?

(A) Sample Mean       (B) Sampling

Option (B) is correct.

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Time Series Multiple Choice Questions and answers (mcqs)

 1- Arrangement of data according to time period is called as: ?

(A) Time Series         (B) Seasonal Variation

Option (A) is correct.

2- Graph of Time Series in which Time period is taken along x-axis and Values along y-axis is called as: ?

(A) Histogram          (B) Historigram

Option (B) is correct.

Note: But, Histogram: Graph of Adjacent Rectangles in which Class Boundaries are taken along x-axis and frequency along y-axis is called as Histogram.

3- Ups and Downs (Fluctuations) in Time Series are: ?

(A) Components of Time Series   (B) Irregular Variations

Option (A) is correct.

4- TCSI abbreviated as: ?

(A) Secular Trend; Cyclic; Seasonal; Irregular  (B) Nothing

Option (A) is correct.

5- The Variations which are caused by Religious Festivals, and Traditions are called as: ?

(A) Cyclic Variations   (B) Seasonal Variations

Option (B) is correct.

6- The life of a Buisness man is an Example of: ?

(A) Cyclic Variations   (B) Secular Trend

Option (A) is correct.

7- The Process of removing trend from time series is defined as: ?

(A) Deseasonalization  (B) Detrending

Option (B) is correct.

Note: Must remember that the process of removing seasonal effect from time series is called as Deseasonalization.

8- From Additive Model; Y = T + C + S + I, we can isolate any component by: ?

(A) Method of Subtraction (B) Method of Division 

Option (A) is correct.

Note: But, From Multiplicative Model; Y = TCSI, we can isolate any component by the Method of Division. For example, Y = TCSI/C = TSI.

9- Parabola is always has: ?

(A) Second Degree          (B) First Degree

Option (A) is correct.

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Curve Fitting by Least Squares Multiple Choice Questions and answers (mcqs)

 1- A linear Curve is: ?

(A) Y = a + b X       (B) Y = ab

Option (A) is correct.

Note: You already know that ' Y = a + b X ' is also a Regression line.

2- The Equation of Hyperbola is: ?

(A) 1/B = X            (B) 1/Y = a + b X

Option (B) is correct.

3- We fit an Exponential Curve If the first differences of the Logarithms are approximately: ?

(A) Constant          (B) Variable

Option (A) is correct.

4- For better the Fit, The Sum of Squares must be: ?

(A) Bigger              (B) Smaller 

Option (B) is correct.

5- Non-Linear Form is: ?

(A) 1/Y = a + b/1 + X     (B) Y = a + b X

Option (A) is correct.

6- Logistic Curve has _ different Stages: ?

(A) 4                      (B) 3

Option (A) is correct.

Note: Must focus on that's, Logistic Curve has Stages; 1- Period of relatively slow growth, 2- Period of accelerated growth, 3- Period of Decelerated growth, 4- Period of Stability.

7- We Fit a Reciprocal line 1/Y = a + b X, If the reciprocals of data show a _ when plotted in a graph: ?

(A) Regression line     (B) Straight line

Option (B) is correct.

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Multiple Regression and Correlation Multiple Choice Questions and answers (mcqs)

 1- The relationship between any two variables by neglecting the effect of other variable is called as: ?

(A) Partial Correlation     (B) Multiple Correlation

Option (A) is correct.

2- The relationship between a Variable and a Combined Variable is called as: ?

(A) Multiple Correlation  (B) Multiple Regression

Option (A) is correct.

3- In Y = a + b1 X1 + b2 X2 ; X1 and X2 are: ?

(A) Dependent Variables  (B) Independent Variables

Option (B) is correct.

Note: Must remember that here "Y" is Dependent Variable.

4- Multiple Correlation Coefficient is denoted by: ?

(A) R1.23               (B) r1.23

Option (A is correct.

5- The Coefficient of Partial Correlation is denoted by: ?

(A) R12.3               (B) r12.3

Option (B) is correct.

6- The Coefficient of Multiple Correlation is denoted as: ?

(A) Ry.12                (B) ry.12

Option (A) is correct.

7- A Regression which have two or more Independent Variables is defined as: ?

(A) Multiple Regression (B) Simple Regression

Option (A) is correct.

Note: But, If Regression have just One Independent Variable is called as Simple Regression.

8- The Coefficient of Multiple Determination lies between: ?

(A) 2 and 3            (B) 0 and 1

Option (B) is correct.

Note: Must focus on that's point ; The Range of Multiple Correlation Coefficient is 0 and 1 also.

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Simple Regression and Correlation Multiple Choice Questions and answers (mcqs)

 1- Dependence of one Variable on other Independent Variable is called as: ?

(A) Regression   (B) Correlation 

Option (A) is correct.

Note: Y = a + bX is a Regression Line. Must remember that 'Y' is a Dependent Variable and 'X' is an Independent Variable. Next, 'a' and 'b' are Least-Squares Estimates.

2- The Independent Variable is called as: ?

(A) Regressand    (B) Regressor 

Option (B) is correct.

3- Regressand is also called as: ?

(A) Predictand      (B) Predictor 

Option (A) is correct.

Note: Must note that's points......

Dependent Variable is called as Regressand, Predictand, Explained Variable. But, Independent Variable is called as Regressor, Predictor, Explanatory Variable.

4- Inexact Relationship is also defined as: ?

(A) Mathematical Relationship  (B) Probabilistic Relationship

Option (B) is correct.

5- Explained Variation + Unexplained Variation = ?

(A) Total Variation   (B) Co-efficient of Variation

Option (A) is correct.

6- Relationship between two Variables is called as: ?

(A) Regression      (B) Correlation

Option (B) is correct.

7- When r = +1, then Correlation is: ?

(A) Perfect Positive   (B) Perfect Negative

Option (A) is correct.

Note: But, When r = - 1, then correlation is perfect negative.

8- Correlation Coefficient 'r' lies between: ?

(A) -2 & +2    (B) -1 & +1

Option (B) is correct.

Note: Correlation Co-efficient 'r' is Independent of  change of Origin and Scale.

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Continuous Probability Distributions (Normal Distribution) Multiple Choice Questions and answers (mcqs)

 1- In 52 cards, Diamonds and Spades are: ?

(A) 13       (B) 6

Option (A) is correct.

Note: Ace and kings are 4.

2- Bernoulli's Distribution has range from: ?

(A) 0,1,2,3,.....,n   (B) 0,1

Option (B) is correct.

3- The Mean of Bernoulli's Distribution is: ?

(A) p         (B) pq

Option (A) is correct.

4- A distribution for which probability is same for each value of success is called as: ?

(A) Bernoulli's Distribution (B) Uniform Distribution

Option (B) is correct.

5- The Function of Uniform Distribution is: ?

(A) P(X) = 1/k   (B) P(X) = k

Option (A) is correct.

6- In Sequence, 1 + 2 + 3 +.....+ n =: ?

(A) n/2           (B) n(n+1)/2

Option (B) is correct.

7- The Mean of Uniform Distribution is: ?

(A) k + 1/2      (B) k/2

Option (A) is correct.

8- Poisson Distribution and Normal Distribution are the Limiting Functions of: ?

(A) Binomial Distribution (B) Bernoulli's Distribution

Option (A) is correct.

9- Standard Normal Variable 'Z' is equal to: ?

(A) X/sigma     (B) X - Mean/sigma

Option (B) is correct.

10- Normal Distribution has range from: ?

(A) - infinity to + infinity    (B) 0 to infinity

Option (A) is correct.

11- Mean Deviation of Normal Distribution is: ?

(A) 4/5 sigma or 0.7979 sigma   (B) 2/3 sigma or 0.6745 sigma

Option (A) is correct.

Note: Must remember that Quartile Deviation of Normal Distribution is 2/3 sigma or 0.6745 sigma.

12- The Total Area under Normal Curve is always: ?

(A) 2           (B) 1

Option (B) is correct.

Note: Many people ask that how can we explain " Total area under normal curve is 1".?

Very easy and simple answer :  0.5 + 0.5 = 1.

13- The Shape of Normal Distribution is: ?

(A) Bell Shaped    (B) Square Shaped

Option (A) is correct.

14- Percentage area between Mean - sigma  and Mean + sigma is: ?

(A) 95.45 %       (B) 68.67 %

Option (B) is correct.

Note: But, Percentage area between Mean - 2 sigma and Mean + 2 sigma is 95.45 %. And, Percentage area between Mean - 3 sigma and Mean + 3 sigma is 99.73 %.

15- When sample size "n" is very large and neither "p" nor "q" is very small, that's called as: ?

(A) Normal Distribution   (B Poisson Distribution

Option (A) is correct.

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Discrete Probability Distributions Multiple Choice Questions and answers (mcqs)

 1- All Trials are Independent in: ?

(A) Binomial Experiment (B) Hypergeometric Experiment

Option (A) is correct.

Note: But, all Trials are Dependent in Hypergeometric Experiment.

2- In Binomial Experiment, drawing is done: ?

(A) With Replacement (B) Without Replacement

Option (A) is correct.

Note: But, In Hypergeometric Experiment, drawing is done Without Replacement.

3- Binomial Distribution has range from: ?

(A) 0,1,2,.....infinity (B) 0,1,2,......n

Option (B) is correct.

Note: Must remember that also Hypergeometric Distribution has range from 0,1,2,......n.

4- The Probability of failure 'q' is equal to: ?

(A) 1- p (B) 1-q

Option (A) is correct.

5- The Variance of Binomial Distribution is: ?

(A) npq (B) np

Option (A) is correct.

Note: But, In Binomial Distribution, Mean = np.

6- For Negative Binomial Distribution, Mean and Variance have a relation: ?

(A) Mean > Variance (B) Mean < Variance 

Option (B) is correct.

Note: Must focus on that's, In Binomial Distribution, always Mean > Variance.

7- The Mean of Hypergeometric Probability Distribution is: ?

(A) nk/N (B) npq

Option (A) is correct.

8- In Hypergeometric Probability Distribution, Probability 'p' is equal to : ?

(A) k/N   (B) k/n

Option (A) is correct.

Note: Attention!!

Now, I am going to tell you most Important points which nobody tells you about that. Must remember that In sense of Problems solving, In case of With Replacement , always use the formula of Binomial Distribution. But, In case of Without Replacement , always use the formula of Hypergeometric Distribution.

9- If 'n' becomes very large and the probability of success "p" is very small, then that's type of Distribution is defined as: ?

(A) Normal Distribution (B) Poisson Distribution

Option (B) is correct.

Note : For example, in problems solving,, n=500 and p=0.01. then we always use Poisson Distribution.

10- In Poisson Distribution, Mean and Variance have a relation: ?

(A) Mean = Variance (B) Mean < Variance

Option (A) is correct.

Note: Must remember that In Poisson Distribution, Mean = np and Variance = np.

11- The Product of N and P(X) ; NP(X) is equal to: ?

(A) Expected Frequency (B) Observed Frequency

Option (A) is correct.

12- In Poisson Process, Average number of occurances per unit time is equal to: ?

(A) Lemda (B) t

Option (A) is correct.

Note: t shows 'time interval".

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Random Variables Multiple Choice Questions and answers (mcqs)

 1- Number of heads when when we toss some coins is an example of: ?

(A) Discrete Random Variable (B) Continuous Random Variables

Option (A) is correct.

Note: Must remember that Discrete Random Variable has Countable Number of Values. But, Continuous Random Variable has Uncountable Number of Values. Here, Option (A) is correct because we can count "Number of Heads when we toss 2 or more coins.

2- Lengths, Widths is an example of: ?

(A) Discrete Random Variable (B) Continuous Random Variable

Option (B) is correct.

3- A variable which can assume values of random experiment is called as:

(A) Random Variable (B) Random Experiment

Option (A) is correct.

4- Probability Distribution is also called as:

(A) Distribution Function (B) Probability Mass Function

Option (B) is correct.

Note: Q- What is Probability Distribution?

An arrangement of probabilities against each possible value of discrete random variable is called as Probability Distribution.

5- Distribution Function , F(x) =: ?

(A) P(X<x) (B) f(x)

Option (A) is correct.

Note: In reality,  P(X<x) that is; Probability of ( X less than and equal to x).

6- Distribution Function is also defined as: ?

(A) Cumulative Probability Distribution (B) Probability Mass Function

Option (A) is correct.

7- Probability Density Function is always: ?

(A) Discrete (B) Continuous

Option (B) is correct.

Note: Probability Density function is denoted as " f(x)" .

8- Expectation E(X) = ?

(A) Sum of X.P(X) (B) Nothing

Option (A) is correct.

9- E(aX + b) =: ?

(A) aE(X) + b (B) E(x) + b

Option (A) is correct.

Note: Must remember that Most Important point which nobody tells you about that, " Mean = Expectation ". Next, Mean of "a" = E(a) = a. that is; Expectation of a constant value is equal to constant itself.

10- Probability Distribution for only two variables at a time is called as: ?

(A) Bi-Variate Probability Distribution (B) Joint Probability Distribution

Option (A) is correct.

Note: But, Probability Distribution for two or more than two variables is called as Joint Probability Distribution. Must focus on that point " Bi-Variate Probability Distribution = Joint Probability Distribution because both distributions have two variables. When we check that it has three variables then it must be purely 'Joint Probability Distribution' .

11- Two random variables X and Y will be Independent If: ?

(A) f(X,Y) = g(X).h(Y)  (B) f(X,Y) = f(X)

Option (A) is correct.

Note: But, If two random variables X and Y will be Dependent then " f(X,Y) does not equal to g(X).h(Y).

12- Covariance of X and Y ; Cov(X,Y) and Correlation Coefficient are zero, When 

(A) X and Y are Independent (B) X and Y are Dependent

Option (A) is correct.

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Probability Multiple Choice Questions and answers (mcqs)

 1- Any particular performance of random experiment is called as:

(A) Trial (B) Sample Space

Option (A) is correct.

2- In S = { 1,2,3,4,5,6} ;  1,2,3,4,5,6 are:

(A) Outcomes (B) Events

Option (A) is correct.

Note: 1,2,3,4,5,6 are the results of random experiment which are called outcomes.

3- Simple Event always have _ outcomes:?

(A) triple outcomes (B) single outcome

Option (B) is correct.

Note: Suppose, A = {1} which have a single outcome is defined as simple event. But, If we suppose, A = {1,2} then set A is defined as Compound event because it has more than 1 outcomes.

4- Exhaustive Events is defined as:

(A) A U B = S (B) AB = S

Option (A) is correct.

Note: The Union of two events A & B is equal to Sample Space 'S' is defined as Exhaustive Events.

5- The Sum of Probability never exceeds:

(A) 2 (B) 1

Option (B) is correct.

6- Given A = { 1,2 }, B = { 4,5,6 } ; A and B are called:

(A) Equally Likely Events (B) Mutually Exclusive Events

Option (B) is correct.

Note: Let's suppose, A = {1,2} , B = {4,5,6}. You can check that both have no common points. So, must remember that The Events A and B which have no common points are called as Mutually Exclusive Events.

But, Let's suppose , A = {2,4,5} and B ={4,5,6} ; Both have common points. So, must remember that The Events which have common points are called as Equally Likely Events.

7- Probability of Sample Space; P(S) = : ?

(A) 1 (B) 0

Option (A) is correct.

Note: Suppose that A = {4,6,2,3,1,5}, For one Dice, S = {1,2,3,4,5,6}, P(S) = number in A/number in Sample Space , that is; P(S) = n(A)/n(S)= 6/6 = 1.

8- Given ; A = {7,8,9} , S = {1,2,3,4,5,6}; P(A) =: ?

(A) 2/3 (B) 1/2

Option (B) is correct.

Note: P(A) = n(A)/n(S) = 3/6 = 1/2.

9- If A and B are independent then P(A intersection B) =: ?

(A) P(A) . P(B) (B) P(A) + P(B)

Option (A) is correct.

10- In Independent Events, drawing is done: ?

(A) Without Replacement (B) With Replacement 

Option (B) is correct.

Note: But, In Dependent Events, drawing is done Without Replacement.

11- Permutation is always in:

(A) Ordered (B) Disordered

Option (A) is correct.

Note: But, Combination is Disordered.

12- If A and B are Mutually Exclusive , then P(A U B)=: ?

(A) P(A) + P(B) (B) P(A) . P(B)

Option (A) is correct.

13- Poker hand shows:

(A) cards (B) Drawn Cards

Option (B) is correct.

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Index Numbers Multiple Choice Questions and answers (mcqs)

 1- The formula of  link relatives is:

(A) Pn/Pn-1 * 100 (B) Pn/Po * 100

Option (A) is correct.

Note: Formula of Price relative is : Pn/Po * 100.

Formula of Quantity relative is : Qn/Qo * 100.

Pn is the price of current year & Po is the price of base year.

2- In Fix-Base Method, we calculate:

(A) Price Relatives (B) Quantity Relatives

Option (A) is correct.

Note: But, In Chain-Base Method , we calculate Link Relatives and then make chain indices.

3- Index number for base period is always taken as:

(A) 200 (B) 100

Option (B) is correct.

4- The formula of Fisher's 'Ideal' Price Index is:

(A) Pon = Square Root of L * P (B) Pon = L * P

Option (A) is correct.

Note: L shows Laspeyre's Price Index and P shows Paasche's Price Index.

5- Value Relative =:

(A) Price Relative * Quantity Relative (B) Nothing

Option (A) is correct.

6- In Time-Reversal Test, Pon * Pno =:

(A) 2 (B) 1

Option (B) is correct.

7- In Tests of Index numbers , we neglect the factor:?

(A) 100 (B) 300

Option (A) is correct.

8- In Factor- Reversal Test, Price Index * Quantity Index = :?

(A) Weighted Index (B) Value Index

Option (B) is correct.

9- Only Fisher's Index satisfies:

(A) Factor Reversal Test (B) Circular Test

Option (A) is correct.

10- In Circular Test, Pab * Pbc * Pca = :?

(A) 100 (B) 1

Option (B) is correct.

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More Multiple Choice Questions and answers are available here!

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