QTM Objective Set 6

Q1. Which of the following is not correct about construction of bar charts?

a. All bars should rise from the same base line

b. Width of the bar should be proportional to the data represented

c. The bars should be arranged from the left to right

d. Length of the bars should be proportional to the data represented

Answer

Ans: b. Width of the bar should be proportional to the data represented

Q2. Which of the following is not true about mean absolute deviation :-

a. Mean deviation is obtained by calculating the absolute deviations of each observation from mean

b. Mean deviation is a more comprehensive measure compared to range

c. It is conducive to further algebraic treatment

d. It cannot be computed for distributions with open end classes.

Answer

Ans: a. Mean deviation is obtained by calculating the absolute deviations of each observation from mean

Q3. The value index number measures the–

a. Changes in prices of a basket of commodities from one period to another

b. Changes in quantities consumed of a basket of commodities over a period of time

c. Change in the total monetary value of a basket of commodities over a period of time

d. Change in the retail prices of various commodities

Answer

Ans: c. Change in the total monetary value of a basket of commodities over a period of time

Q4. A market researcher wants to find out the buying behavior of the typical household during the weekends. He divides the city into various localities such that each locality represents the city population in terms of age group, gender and social status. Then he randomly selects five localities and surveys each household. Which of the following sampling techniques best describes the method used by the researcher:-

a. Cluster sampling

b. Systematic sampling

c. Stratified sampling

d. Convenience sampling.

Answer

Ans: a. Cluster sampling

Q5. If every item in the data set is increased by the same quantity then the standard deviation of the data set–

(a) Remains the same

(b) Increases by the same quantity by which every data item is increased

(d) Increases by the square root of the same quantity by which every data item is increased

Answer

Ans: (a) Remains the same

Q6. Which of the following is true with regard to a linear equation Y – a – bX = 0, where X is the independent variable and Y is the dependent variable:-

(a) The slope of the straight line is ‘a’

(b) The Y-intercept of the straight line is 0

(d) The slope and the Y-intercept remain constant for all combinations of X and Y values which satisfy the equation

Answer

Ans: (d) The slope and the Y-intercept remain constant for all combinations of X and Y values which satisfy the equation

Q7. Which of the following quantitative method is not used by managers to take decision:-

(a) Linear programming

b) Time series

c) Regression analysis

d) Hypothesis testing

Answer

Ans: (a) Linear programming

Q8. In the graphical method of solving linear programming problems the feasible region is the set of all points–

a) Which does not satisfy any of the constraints?

b) Which satisfy exactly one of the constraints?

c) Which satisfy all the constraints?

d) At which the objective function has the same value?

Answer

Ans: c) Which satisfy all the constraints?

Q9. Which of the following is false in regard to histogram :-

a) The class intervals are represented by the base of the rectangles

b) The frequencies are represented by the heights of the rectangle

c) If the class intervals are of equal width then the bases of the rectangles will be equal in length

d) The tallest rectangle in a histogram represents the class interval with the lowest frequency

Answer

Ans: d) The tallest rectangle in a histogram represents the class interval with the lowest frequency

Q10. Which of the following measures in not affected by the presence of extreme values in a dataset :-

a) Range

b) Arithmetic mean

c) Standard deviation

d) Median

Answer

Ans: d) Median

Q11. 12x + 1/3y – 1/3z = -1

1/3x – 1/2y -1/6z = 4

1/6x – 5/6y + 1/2z = 3

The values of x in the above simultaneous equations would be–

Answer

Ans: 6

Q12. The following details are available with regard to a data set: Sx = 33, Sx² = 199,

n = 6. If each observation in the data set is multiplied by 2 then the standard deviation of the resulting values will be equal to:

a) (35/3)1/2

b) 35/3

c) 3

d) 25

Answer

Ans: a) (35/3)1/2

Q13. The following data pertains to three commodities:-

The base year is 1994. The unweighted aggregates price index for the year 2004 is approximately–

115.62
125.45
134.21
250.55

Answer

Ans: 134.21

Q14. If the regression equation is the perfect estimator of the dependent variable then which of the following is false?

a) The standard error of estimate is zero

b) The coefficient of correlation is zero

c) The coefficient of determination is 1.00

d) All the data points fall on the regression line

Answer

Ans: b) The coefficient of correlation is zero

Q15. If the regression equation is a perfect estimator of the dependent variable then which of the following is false :-

a) The standard error of estimate is zero

b) The coefficient of correlation is zero

c) The coefficient of determination is 1.00

d) All the data points fall on the regression line

Answer

Ans: b) The coefficient of correlation is zero

Q16. Which of the following represents the proportion of variation in the dependent variable that is explained by the regression line :-

a) Coefficient of determination

b) Coefficient of correlation

c) Coefficient of variation

d) Standard error of estimate

Answer

Ans: a) Coefficient of determination

Q17. If the coefficient of correlation between the two variables lies between -1 and 0, then the covariance between them is–

a) Positive

b) Negative

c) Zero

d) Equal in magnitude to the variances of both the variables

Answer

Ans: b) Negative

Q18. If b_YX is the slope of coefficient of regression line of Y on X, and b_XY is the slope coefficient of regression line of X on Y then which of the following is true :-

a) b_YX is positive implies that b_XY is positive

b) bYX is positive implies that bXY is negative

c) b_YX and b_XYare reciprocals

d) The product of b_YX and b_XY is zero

Answer

Ans: b) bYX is positive implies that bXY is negative

Q19. A graphical method of representing states of nature and courses of action involved in decision making is referred to as–

a) Decision tree

b) Histogram

c) Scatter diagram

d) Frequency distribution

Answer

Ans: a) Decision tree

Q20. If the probability of occurrence of one event is not affected by the occurrence of another event and vice versa then the two events are said to be–

a) Collectively exhaustive

b) Independent

c) Dependent

d) Mutually exclusive

Answer

Ans: b) Independent

Q21. Bayes’ theorem helps the statistician to calculate—

a) Dispersion

b) Subjective probability

c) Posterior probability

d) Classical probability

Answer

Ans: c) Posterior probability

Q22. In a binomial distribution the probability of getting zero or more numbers of successes is equal to–

a) 0

b) 1

c) The probability of getting zero success

d) The probability of getting successes in all trials

Answer

Ans: b) 1

Q23. Which of the following measures represent the scatter of the values in a data set :-

a) Arithmetic mean

b) Geometric mean

c) Standard deviation

d) Median

Answer

Ans: c) Standard deviation

Q24. As the sample size increases–

a) The variation of the sample mean from the population mean becomes larger

b) The variation of the sample mean from the population mean becomes smaller

c) The variance of the sample becomes less than the variance of the population

d) The standard deviation of the sample becomes more than the standard deviation of the population.

Answer

Ans: b) The variation of the sample mean from the population mean becomes smaller

Q25. In the graphical method of solving linear programming problems if there is a unique optimal solution, then the optimal solution–

a) Is always found at the center of the feasible region

b) Is always at the origin

c) Lies outside the feasible region

d) Is located at one of the corner points of the feasible region

Answer

Ans: d) Is located at one of the corner points of the feasible region

Q26. A multiple regression equation has–

a) Multiple dependent variables

b) One independent variable

c) One dependent variable

d) A standard error of estimate equal to zero

Answer

Ans: c) One dependent variable

Q27. Which of the following conditions indicate the existence of multiple optimal solutions when a linear programming problem is solved by the graphical method :-

a) One of the constraints is parallel to the horizontal axis

b) The objective function is parallel to the vertical axis

c) The objective function is parallel to one of the edges of the feasible region which is in the direction of optimal movement of the objective function

d) If two or more constraints are parallel to each other

Answer

Ans: c) The objective function is parallel to one of the edges of the feasible region which is in the direction of optimal movement of the objective function

Q28. Three persons enter into a railway carriage and there are 8 seats available. In how many ways they can seat themselves?

a) 24

b) 336

c) 40

d) 56

Answer

Ans: b) 336

Q29. In which of the following the simple harmonics mean is appropriate:

a) A set of ratios using the numerators of the ratio data as weights

b) A set of ratios using the denominators of the ratio data as weights

c) A set of ratios which have been calculated with the same numerators

d) A set of ratios which have been calculated with the same denominators

Answer

Ans: c) A set of ratios which have been calculated with the same numerators

Q30. Which of the following statements is not true about standard deviation?

a) Combined standard deviation of two or more groups can be calculated

b) The sum of the squares of the deviations of items of any series from a value other than the arithmetic mean would always be smaller

c) Standard deviation is independent of any change of origin

d) Standard deviation is dependent on the change of scale

Answer

Ans: b) The sum of the squares of the deviations of items of any series from a value other than the arithmetic mean would always be smaller

Q31. Which of the following is/are true with respect to geometric mean :-

(a) Geometric mean cannot be calculated if any of the value in the set is zero.

(b) Geometric mean is appropriate for averaging the ratios of change, for average of proportions, etc.

Only (I) above

Only (II) above
All (I), (II) and (III) above
Only (II) above

Answer

Ans: Only (I) above

Q32. The probability of getting two heads from three tosses of a fair coin is–

a) 1/8

b) 1/4

c) 3/8

d) 1/2

Answer

Ans: c) 3/8

Q33. If A and B are two mutually exclusive events and P(A) = 2/3, then the probability of events A and B happening together is–

a) 0

b) 1/3

c) 2/3

d) 1/2

Answer

Ans: a) 0

Q34. Which of the following can be directly used as the test statistic in hypothesis tests on the basis of non standardized scale :-

(a) The sample mean, when the test involves the population mean.

(b) The difference between two sample means, when the tests involve the difference between two population means.

Only (a) above
Only (b) above
Only (c) above
All (a), (b), (c) above

Answer

Ans: All (a), (b), (c) above

Q35. A box contains 60 ball point pens out of which 10 pens are defective. 8 pens are randomly picked up from the box. The probability distribution of the number of pens which are randomly picked, will be–

a) A discrete uniform distribution

b) A binomial distribution

c) A hyper geometric distribution

d) A Chi- square distribution

Answer

Ans: b) A binomial distribution

Q36. If we consider the process of selecting a simple random sample as an experiment then which of the following can be treated as random variable(s)?

(a) Sample mean

(b) Sample standard deviation

(d) Sample median

(i) Only (a) above

(ii) Only (b) above

(iii) All (a), (b), (c), (d) above

(iv) Only (d) above

Answer

Ans: (iii) All (a), (b), (c), (d) above

Q37. The covariance of random variable with itself is always–

a) A positive quantity

b) A negative quantity

c) 0

d) Less than its expected value

Answer

Ans: a) A positive quantity

Q38. A man has 6 friends. In how many ways he can invite one or more of them to a party?

a) 63

b) 64

c) 119

d) 120

Answer

Ans: a) 63

Q39. Find x; if logx/log2 = log36/log4

a) 0

b) 2

c) 4

d) 6

Answer

Ans: d) 6

Q40. The empirical relationship between range (R) and mean deviation (M.D) is–

a) 2R=15M.D

b) 3R=17M.D

c) R=17M.D

d) 3R=M.D

Answer

Ans: b) 3R=17M.D

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