Q1. If A and B are independent events with P (A) = 0.25, P (B) =0.4 and P (A UB) = 0.5, then, P (A/B) & P (B/A) are
a. 0.25 & 0.4
b. 0.600 & 0.275
c. 0.725 & 0.275
d. 0.650 & 0.650
e. 0.542 & 0.335
Answer
Ans: a. 0.25 & 0.4
Q2. If you want to test the whether the change is significant on the mean body weight on group of randomly chosen people after a particular diet is administered, you should employ
a. Paired-t test
b. A simple t test
c. An independent single sample t test
d. An independent two sample t test
e. Variance test
Answer
Ans: a. Paired-t test
Q3. Cluster sampling is
a. a non-probability sampling method
b. the same as convenience sampling
c. a probability sampling method
d. Judgement sampling
e. None of these alternatives is correct.
Answer
Ans: c. a probability sampling method
Q4. A LP problem has 3 decision variables and 5 constraints. How many non basic variables are there?
a. 3
b. 5
c. 8
d. 7
e. 2
Answer
Ans: a. 3
Q5. If a random variable X is distributed normally with mean 30 and variance 25, find oi
P(X>40)
a. 0.2220
b. 0.0228
c. 0.0954
d. 0.0233
e. 0.0919
Answer
Ans: b. 0.0228
Q6. A sampling method in which the population is divided into groups such that each group has a small variation with in itself and a wide variation between themselves and samples are drawn from each group is known as
a. Random sampling
b. Stratified sampling
c. Cluster sampling
d. Systematic sampling
e. Judgmental sampling
Answer
Ans: b. Stratified sampling
Q7. The following linear trend expression was estimated using a time series with 17 time periods.
Tt= 129.2 + 3.8t
The trend projection for time period 18 is
a. 68.4
b. 193.8
c. 197.6
d. 6.84
e.19.38
Answer
Ans: c. 197.6
Q8. If the sampling fraction n/N is less than 0.05, the standard error of the sample mean is given by
a. σ / √ n
b. σ / √n x √[(N- n)/(N- 1)
c. σ / √n x √(N/n)
d. σ / √n x √[(N-1)/(N- n)
Answer
Ans: a. σ / √ n
Q9. The sample mean is the point estimator of : Ans (Population mean µ)
a. x
b. g
C. X
d.p e. S
Answer
Ans: a. x[
Q10. A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation
Y$ = 30,000 + 4 X
The above equation implies that an
a. Increase of $4 in advertising is associated with an increase of $4,000 in sales
b. Increase of $1 in advertising is associated with an increase of $4 in sales
c. Increase of $1 in advertising is associated with an increase of $34,000 in sales
d. Increase of $1 in advertising is associated with an increase of $4,000 in sales
e. Increase of $4 in advertising is associated with an increase of $30,000 in sales
Answer
Ans: b. Increase of $1 in advertising is associated with an increase of $4 in sales
Q11. A random Variable has the following probability distribution:
X P(X)
- 0.05
- 0.1
- 0.15
- 0.20
- 0.25
- 0.10
- 0.15
What is the value of P(l<= X<=5)?
a. 0.80
b. 0.25
c. 0.15
d. 0.10
e. 0.30
Answer
Ans: a. 0.80
Q12. Two cards are drawn without replacement from a deck of 52 cards. What is the probability of drawing two queens?
a. 1/221
b. 1/121
c. 1/321
d. 1/421
e. 1/111
Answer
Ans: a. 1/221
Q13. Assume a binomial probability distribution with n = 40 and p = .55. Compute the mean and standard deviation of the random variable.
a. Mean = 22 and SD = 3.146
b. Mean = 20 and SD = 3.146
c. Mean = 24 and SD = 3.146
d. Mean = 26 and SD = 3.146
e. Mean= 18 and SD = 3.146
Answer
Ans: a. Mean = 22 and SD = 3.146
Q14. From a calendar for 2005 we sample every 11th day starting from January 7th; what type of sampling is this?
a. Judgemental sampling
b. Simple random sampling without replacement
c. Systematic sampling
d. Cluster sampling
e. Simple random sampling with replacement
Answer
Ans: c. Systematic sampling
Q15. In a goodness-of-fit test where the sample size is 200, there are 5 categories, and the significance level is .05. The critical value of %2 is
a. 9.488
b. 11.070
c. 43.773
d. 45.887
e. 25.669
Answer
Ans: a. 9.488
Q16. To conduct the sign test, we assume
a. The population is normally distributed
b. The scale of measurement is interval
c. The samples are dependent
d. There are at least 20 observations in the sample
e. There are minimum 25 observations in the sample
Answer
Ans: b. The scale of measurement is interval
Q17. A time series component which cannot be analysed by a mathematical model is:
a. Trend
b. Seasonal
c. Cyclical
d. Random
e. Cyclical and random
Answer
Ans: d. Random
Q18. Which of the following cannot be inferred from a scatter diagram?
a. Cause effect relationships
b. Presence or absence of relationships
c. Linear or curvilinear relationship
d. Direct or inverse relationship
e. All can be studied
Answer
Ans: a. Cause effect relationships
Q19. Which of the following is true of the coefficient of determination?
a. It is the square of the correlation coefficient
b. It conveys the extent to which the variations are explained by the regression equation
c. It conveys the extent to which the variations are unexplained by the regression equation
d. Both (a) and (b) above
e. Both (a) and (c) above
Answer
Ans: d. Both (a) and (b) above
Q20. When formulating Transportation LP problems, constraints usually deal with:
a. The number of items to be transported
b. The shipping costs associated with transporting goods
c. The distance goods are to be transported
d. The number of origins and destinations
e. The capacities of origins and requirements of destinations
Answer
Ans: d. The number of origins and destinations
Q21. If the coefficient of correlation between two variables X and Y is equal to one, then there is
a. No relationship between variables X and Y
b. A perfect positive linear relationship between variables X and Y
c. A perfect negative linear relationship between variables X and Y
d. A cause and affect relation exists between X and Y
e. A weak association between variables X and Y
Answer
Ans: b. A perfect positive linear relationship between variables X and Y
Q22. An inventor claims that her new petrol additive will drastically enhance the mileage of the petrol powered cars. Currently, the vehicle runs as average mileage 15 km for one litre of petrol. The appropriate null and alternative hypotheses in evaluating her claim will be (in the order of HO and Ha)
a. X=15, X> 15
b. X=15,X<15
c. X>15,X=15
d.X=15,X=15
e. X= 15, X = < 15
Answer
Ans: a. X=15, X> 15
Q23. After deseasonalisation, a time series can be represented as
a. Y = S x C x I
b. Y = TxSxCxI
c. Y = TxCxI
d. Y = TxSxI
e. Y = TXSXC
Answer
Ans: c. Y = TxCxI
Q24. If one regression coefficient is greater than unity then the other must be:
a. Greater than the first one
b. Equal to unity
c. Less than unity
d. Equal to zero
e. Less than the first one
Answer
Ans: c. Less than unity
Q25. Which of the following statements is false?
a. In a proper random sampling, every element of the population has a known (and often equal) chance of being selected
b. The precision of a sample mean or sample proportion depends only upon the sample size (and not the population size) in a proper random sample
c. Convenience sampling often leads to biases in estimates since the sample is often not representative of the population
d. If a sample of 1000000 families is randomly selected from all of Kota (with about 8000000 families) and the average family income is computed, then the true value of the family income for all families in Kota is known
e. None of the above
Answer
Ans: e. None of the above
Q26. For two variables x and y to be independent of each other which of the following must be true
a. xy
b. xy
c. Cov (x, y) = 0
d.
=
e. E(x) = E(y)
Answer
Ans: d.
=
Q27. Which of the following is a true measure of regret?
a. Maximum possible profits – realized profits
b. Maximum of minimum profits – minimum of minimum profits
c. Maximum possible profits – foregone profits (probably)
d. Maximum of maximum profits – maximum of minimum profits
e. Maximum possible profits – minimum of maximum profits.
Answer
Ans: c. Maximum possible profits – foregone profits (probably)
Q28. A sample of 15 is drawn from a population size of 100. The finite population correction factor is
a. 0.150
b. 0.184
c. 0.523
d. 0.834 (I think it should be 0.86)
e. 0.9266
Answer
Ans: d. 0.834 (it should be 0.86)
Q29. Which of the following represents repetitive and predictable movements around the trend line within a time period of one year or less?
a. Secular trend
b. Cyclical fluctuation
c. Seasonal variation
d. Irregularvariation
e. Temporary variation.
Answer
Ans: c. Seasonal variation
Q30. Which of the following is true with respect to the method of least squares?
a. Sum of the squared values of the horizontal distances from the regression line to the y-axis and the corresponding points of the dependent variable is minimized
b. Sum of the squared values of the vertical distances from the regression line to the x-axis and the corresponding points of the independent variable is minimized
c. Sum of the squared values of the horizontal distance from each plotted point based on the observations to the regression line is minimized
d. Sum of the squared values of the vertical distance from each plotted point to the regression line is minimized
e. None of the ab ove.
Answer
Ans: d. Sum of the squared values of the vertical distance from each plotted point to the regression line is minimized
Q31. The probability that an observation, following a normal distribution, will lie within [i
± 1.3a is
a. 9.5 %
b. 19.0%
c. 40.3%
d. 50.0%
e. 80.6%
Answer
Ans: e. 80.6%
Q32. Arrivals of customers at an ATMs follow the Poisson distribution. The average arrivals per hour is 6. The probability of exact 6 arrivals in an hour is
a. 1.00
b. 0.50
c. 0.25
d. 0.16
e. 0.10
Answer
Ans: d. 0.16
Q33. If a random sample of size 15 is selected from a symmetrical population with a unique mode, the degrees of freedom of the observation is
a. 14
b. 15
c. 16
d. 17
e. 18
Answer
Ans: a. 14
Q34. In regression analysis, represents how much each unit change of the independent variable changes the dependent variable.
a. Slope
b. Y – intercept
c. Standard error of estimate
d. Dependent variable
e. Coefficient of correlation
Answer
Ans: a. Slope
Q35. If two variables X and Y are perfectly positively correlated and their standard deviations are 5 and 10 respectively, then the covariance is
a. 0.40
b. 0.50
c. 2.00
d. 4.00
e. 50.00
Answer
Ans: e. 50.00
Q36. The sample proportion of ripe mangoes in a large consignment is 0.7. If the upper limit of a confidence interval for the proportion of ripe mangoes in the lot is 0.86, the lower limit is:
a. 0.64
b. 0.54
c. Depends on the confidence level
d. Depends on the sample size
e. Both (c) and (d) above
Answer
Ans: b. 0.54
Q37. A contingency table for two attributes consists of 24 cells. The number of degrees of freedom for the chi square test statistic is:
a. Depends on the number of rows and columns
b. 24
c. 23
d. 14
e. 15
Answer
Ans: a. Depends on the number of rows and columns
Q38. Which of the following statements are true? (I am not sure)
a. When the percent of trend is below 100, the relative cyclical trend is negative and conversely
b. When the percent of trend is below 100, the relative cyclical trend is positive and conversely
c. When the percent of trend is below 100, the relative cyclical trend is negative but not conversely
d. When the percent of trend is below 100, the relative cyclical trend is positive but not conversely
e. The two measures have to be considered independently
Answer
Ans: b. When the percent of trend is below 100, the relative cyclical trend is positive and conversely
Q39. Which of the following is not true of random variations?
a. They can be identified
b. It cannot be explained mathematically
c. They occur in a random manner
d. They cannot be easily predicted
e. All are true
Answer
Ans: a. They can be identified
Q40. The loss from stocking a unit of a product not sold is Rs.30 while the profit from selling a unit of that product is Rs.50. The minimum probability of selling an extra unit that will justify stocking it is:
a. 3/5
b. 2/5
c. 3/8
d. 2/8
e. 3/4
Answer
Ans: d. 2/8
