0710 QM (CFA530)

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    Question PaperQuantitative Methods (CFA530): October 2007

    Answer all questions. Marks are indicated against each question.

    1. Which of the following statements is/are true with regard to the extrapolation in financial analysis?

    I. Forecasting future sales, cost and profit.

    II. Long-term capital requirements.

    III. Production of financial statements for financial institutions, banks, etc.

    (a) Only (I) above

    (b) Only (II) above

    (c) Only (III) above

    (d) Both (I) and (III) above(e) All (I), (II) and (III) above.

    (1 mark)

    2. The sales of a consumer durable are ascertained as follows:

    Year 2000 2001 2002 2003 2005

    Sales Units(in 000 s) 9 11 18 23 31

    Using linear approximation method of interpolation, find the sales in year 2004.

    (a) 24,000 units

    (b) 25,225 units

    (c) 26,750 units

    (d) 27,000 units

    (e) 29,500 units.

    (1 mark)

    3. At K = 17%, the present value of cash flow of a project is Rs.255.76 and at K = 18%, the present value of cash

    flow is Rs.249.19. At what value of K, the present value of cash flow is Rs.250?

    (a) 11.35%

    (b) 15.67%

    (c) 17.88%

    (d) 19.01%

    (e) 21.54%.

    (1 mark)

    4. Which of the following is false regarding the number and size of class intervals?

    (a) Every item of data or data point should be included in one and only one class

    (b) Adjacent classes should not have intervals in between(c) Classes should not overlap

    (d) Class intervals should be of the same length to the extent possible

    (e) The number of classes may be equal to the square of the number of data points.

    (1 mark)

    5. To determine the appropriate width of each class interval in a grouped frequency distribution, we

    (a) Take the square of the number of observations

    (b) Divide the number of desired class intervals by the range of the data(c) Take the square root of the number of observations

    (d) Divide the range of the data by the number of desired class intervals

    (e) Divide the range of the data by 2.

    (1 mark)

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    6. Which of the following is/are true with regard to the negatively skewed distribution?

    I . In negatively skewed distribution curve, the most of the values are concentrated at higher end.

    II. For negatively skewed distribution curve A.M < Median < Mode.

    III. Negatively skewed distribution curve tails off towards the higher end.

    (a) Only (I) above(b) Only (III) above

    (c) Both (I) and (II) above(d) Both (II) and (III) above

    (e) All (I), (II) and (III) above.

    (1 mark)

    7.If m =

    2x 10x 5 + and n = 7x + 3, then m n =

    (a) 3 27x 32x 9x 15 + + (b) 3 27x 35x 7x 18+ + + (c) 3 27x 73x 65x 15+ + + (d) 3 27x 67x 5x 15 + + (e) 3 27x 67x 30x 17. + +

    (1 mark)

    8. Which of the following measures of dispersion is more sophisticated measure of risk, employed commonly in

    finance?

    (a) Range

    (b) Standard deviation

    (c) Mean deviation

    (d) Quartile deviation

    (e) Coefficient of variation.

    (1 mark)

    9. According to Bienayme-Chebyshev rule, at least what percentage of the observations in a distribution of data

    will lie within 3 standard deviations of the mean?

    (a) 25%

    (b) 50%

    (c) 75%

    (d) 89%

    (e) 97%.

    (1 mark)

    10.Which of the following statements is/are true with regard to the computer?

    I. Computer is an electronic device.

    II. Computer can perform long sequences of computations without human interventions.

    III. Computer has the ability of storing and executing a given set of instructions for solving a particular

    problem.

    (a) Only (I) above

    (b) Only (II) above

    (c) Both (I) and (II) above

    (d) Both (II) and (III) above

    (e) All (I), (II) and (III) above.

    (1 mark)

    11.In a venn diagram, usually the sample space will be represented as

    (a) A circle

    (b) A square(c) A rectangle

    (d) A triangle

    (e) An oval.

    (1 mark)

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    12.Which of the following is/are false with regard to the rules of probability?

    I. The probability of the entire sample space is one.

    II. Maximum possible area of an event is one.

    III. The probability of an event can be negative.

    (a) Only (I) above

    (b) Only (II) above

    (c) Only (III) above(d) Both (I) and (II) above

    (e) Both (II) and (III) above.

    (1 mark)

    13.If two balls are drawn from a bag containing 6 red and 9 blue balls, then what is the probability that one is red

    and the other is blue?

    (a) 0.4312

    (b) 0.5143

    (c) 0.6225

    (d) 0.7314

    (e) 0.8256.

    (1 mark)

    14.The probability that A will be alive for 15 years is 0.6 and the probability that B will be alive for 15 years is 0.7.

    What is the probability that both A and B will be alive for 15 years?

    (a) 0.12

    (b) 0.24

    (c) 0.28(d) 0.35

    (e) 0.42.

    (1 mark)

    15.The Central Processing Unit (CPU) consists of

    I. Control Unit.II. Main Memory.

    III. Arithmetic and Logic Unit.

    (a) Only (I) above

    (b) Only (II) above(c) Both (I) and (II) above

    (d) Both (I) and (III) above

    (e) All (I), (II) and (III) above.

    (1 mark)

    16.If the annual growth rates of sales of a factory in 5 years are 3.5%, 5.4%, 6.8%, 7.3% and 6.5% respectively,

    then the compounded growth of output per annum for the given period is

    (a) 5.89%(b) 4.62%

    (c) 3.55%

    (d) 2.13%

    (e) 1.98%.

    (1 mark)

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    17.The following distribution shows the ages of 100 persons in a group:

    Age (in years) Number of persons

    20 25 5

    25 30 13

    30 35 18

    35 40 14

    40 45 1945 50 11

    50 55 7

    55 60 10

    60 65 3

    What is the average age of the persons in the group?

    (a) 21.41

    (b) 25.82

    (c) 37.45

    (d) 40.40

    (e) 45.50.

    (2 marks)

    18.The following details are available with regard to a data set:

    n = 5 ,X = 100 and

    2 2,442X = If each observation in the data set is multiplied by 3, then the standard deviation of the resulting data set will beequal to

    (a) 9.40

    (b) 17.35

    (c) 28.21

    (d) 32.28

    (e) 39.71.

    (1 mark)

    19.Coefficients of variations of two series are 60% and 80%, and their standard deviations are 12 and 18

    respectively. The means of two series are

    (a) 15.5 and 21.0

    (b) 17.0 and 23.5

    (c) 18.5 and 30.0

    (d) 20.0 and 22.5

    (e) 22.0 and 25.4.

    (1 mark)

    20.If the sum of the deviations (taking signs into account) of the items from a measure of central tendency is zero,

    then that measure is known as

    (a) Harmonic mean

    (b) Geometric mean

    (c) Arithmetic mean

    (d) Median

    (e) Mode.

    (1 mark)

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    21.The probability distribution of a random variable X is as follows:

    X 10 14 18 22

    Probability 0.2 0.1 0.4 0.3

    The expected value of X will be equal to

    (a) 11.3

    (b) 15.7(c) 17.2

    (d) 18.6

    (e) 21.4.

    (1 mark)

    22.Consider the following sample of paired observations:

    X 4 4 5 6 7 10

    Y 6 7 5 6 4 2

    The covariance between X and Y is

    (a) 4.5

    (b) 3.8(c) 1.9

    (d) 2.7

    (e) 4.6.

    (2 marks)

    23.Which of the following is/are the categories of decision making?

    I. Decision making under conditions of certainty.

    II. Decision making under conditions of uncertainty.III. Decision making under conditions of risk.

    (a) Only (I) above

    (b) Only (II) above

    (c) Only (III) above(d) Both (I) and (III) above

    (e) All (I), (II) and (III) above.

    (1 mark)

    24.If the decision maker is optimistic, then he is likely to use

    (a) Maximax criterion

    (b) Maximin criterion

    (c) Regret criterion

    (d) Hurwicz criterion

    (e) Heuristic tables.

    (1 mark)

    25.If the marginal profit and marginal loss of a product are Rs.250 and Rs.125 respectively, the probability of sales

    that will justify stocking the product is

    (a) 15%

    (b) 24%

    (c) 29%

    (d) 33%(e) 41%.

    (1 mark)

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    26.In a hypothesis testing, which of the following indicates the power of the test?

    (a) (b) (c) (d) 1 (e)

    1 .

    (1 mark)

    27.If a random sample of size 15 is drawn from a finite population of 65 units without replacement and the

    population standard deviation is 13, then the standard error of the sample mean is

    (a) 0.89

    (b) 1.27

    (c) 2.31

    (d) 2.97

    (e) 3.15.

    (1 mark)

    28.Which of the following is not a type of random sampling?

    (a) Simple random sampling

    (b) Stratified random sampling

    (c) Systematic sampling

    (d) Judgmental sampling

    (e) Cluster sampling.

    (1 mark)

    29.If total sum of squares is 525 and regression sum of squares is 380, then the coefficient of determination is

    (a) 1.9838

    (b) 0.7238

    (c) 2.3438

    (d) 3.0438

    (e) 4.1138.

    (1 mark)

    30.A contingency table prepared for chi-square test contains 3 rows and 4 columns. The degrees of freedom in this

    case will be

    (a) 12

    (b) 11

    (c) 9(d) 8

    (e) 6.

    (1 mark)

    31.Multicollinearity is the

    (a) Existence of correlation among independent variables

    (b) Absence of correlation among independent variables

    (c) Existence of correlation among dependent variables

    (d) Absence of correlation among dependent variables

    (e) Predictive power of the constants.

    (1 mark)

    32.The upper control limit for R chart if n = 5 , R 5.9= , d2 = 2.326 and d3 = 0.864 is

    (a) 12.739(b) 16.826

    (c) 10.125

    (d) 18.224

    (e) 20.478.

    (1 mark)

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    33.Simulation is used under

    (a) Conditions for certainty

    (b) Conditions for uncertainty

    (c) Conditions of risk

    (d) Conditions of known probabilities

    (e) Decision tree analysis.

    (1 mark)

    34.Which of the following techniques is suitable for testing whether there is a significant difference between more

    than two sample means?

    (a) Chi-square test

    (b) Analysis of variance

    (c) Simple regression analysis

    (d) Multiple regression analysis

    (e) Correlation analysis.

    (1 mark)

    35.The managers use sample statistics to estimate

    (a) Sampling distribution(b) Population parameters(c) Sample characteristics

    (d) Population size

    (e) Accuracy of the distribution.

    (1 mark)

    36.A stock broker has identified that 70% of the telephone calls he receives during business hours are for buying or

    selling securities and rest of the calls are for other purposes. What is the probability that out of the first 10

    telephone calls received in a day, exactly six calls are for trading in securities?

    (a) 12%

    (b) 17%

    (c) 20%

    (d) 26%

    (e) 33%.

    (2 marks)

    37.A random sample of 17 people is taken from a group in which 35% favor a particular political stand .What is theprobability that at least 5 individuals in the sample favor this political stand?

    (a) 0.9091

    (b) 0.7652

    (c) 0.6453

    (d) 0.4215

    (e) 0.2315.

    (2 marks)

    38.

    For a simple linear regression equation,( )

    2

    Y Y 157.63 =and there are 13 pairs of observations. The

    standard error of estimate is

    (a) 3.785

    (b) 5.427(c) 6.345

    (d) 9.587

    (e) 12.125.

    (1 mark)

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    39.Consider the following data:

    X 1 2 4 5 6 8 10 12

    Y 2 3 5 6 7 4 3 10

    The correlation coefficient is

    (a) 0.45

    (b) 0.56(c) 0.60

    (d) 0.73

    (e) 0.80.

    (2 marks)

    40.The average height of 500 towers is noted as 180.40 ft. After observing the heights of towers for certain period

    of time, two of them were found to be wrongly taken as 297 ft and 165 ft against their correct height of 197 ft

    and 185 ft respectively. What is the correct average height of the towers?

    (a) 167.00 ft

    (b) 177.60 ft

    (c) 181.90 ft

    (d) 180.24 ft

    (e) 178.65 ft.

    (1 mark)

    41.In how many ways can the letters of the word STRANGE be arranged so that the vowels occupy only the odd

    places?

    (a) 1,200

    (b) 1,440

    (c) 2,200

    (d) 3,780

    (e) 3,840.

    (1 mark)

    42.Four numbers are in A.P. whose sum is 2 and the product of the first and the fourth terms is ten times theproduct of the second and the third terms. The fourth number of the series is

    (a) 1

    (b) 1

    (c) 2

    (d) 3

    (e) Either 4 or 5.

    (2 marks)

    43.A normal variable X has a mean of 96 and a standard deviation of 12. The Z value corresponding to the X value

    of 100 is

    (a) 12

    (b) 96(c) 100

    (d)1

    3

    (e)1

    .36

    (1 mark)

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    44.The following details are available with regard to a right tailed hypothesis test on population mean:

    0HX 527, 56, 525, n 100= = = =

    and significance level is 0.05. It is later known that the true population

    mean is 530. Which of the following can be said with regard to the test?

    (a) t-test should be used

    (b) Test leads to Type I error

    (c) Test leads to Type II error

    (d) Test does not lead to either Type I error or Type II error

    (e) Given information is insufficient to conclude.

    (2 marks)

    45.A finance company offers to pay a sum of Rs.32,000 at the end of 6 years to investors who deposit Rs.4,000annually for 6 years .The implicit interest rate is

    (a) 11.75%

    (b) 12.50%(c) 11.43%

    (d) 10.62%

    (e) 14.15%.

    (2 marks)

    46.If 1 2X 51, X 50= = and 1 2X X

    0.0884

    =, then the value of z-statistic for 0 1 2H : = is

    (a) 10.3122

    (b) 11.3122(c) 12.3122

    (d) 13.3122

    (e) 14.3122.

    (1 mark)

    47.A random sample of size 9 is selected from a symmetrical population with a unique mode. The sample mean and

    standard deviation are 150 and 25 respectively. What is the 95% confidence interval in which the populations

    mean () will lie?

    (a) (120.78, 149.22)

    (b) (125.78, 159.22)

    (c) (130.78, 169.22)

    (d) (135.78, 179.22)

    (e) (140.78, 189.22).

    (2 marks)

    48.Which of the following statements is false?

    (a) If the primal formulation of a linear programming problem is a minimizing problem then the dual

    formulation will be a maximizing problem

    (b) If the primal formulation of a linear programming problem is a maximizing problem then the dual

    formulation will be a minimizing problem(c) The dual formulation is an inverse of the primal formulation in every respect

    (d) The dual formulation cannot be solved for an optimal solution

    (e) The dual formulation can be derived from the same data from which the primal is formulated.

    (1 mark)

    49. 2x 5x 6limx 3x 3

    + =

    (a) 1

    (b) 2

    (c) 3

    (d) 4

    (e) 5.

    (1 mark)

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    50.

    If y =

    x

    x 1+ , then

    dy

    dx for x = 4 is

    (a) 1/25

    (b) 2/32

    (c) 1/27

    (d) 2/45

    (e) 3/52.(2 marks)

    51.The Bayes theorem helps the statistician to calculate

    (a) Subjective probability

    (b) Classical probability

    (c) Posterior probability

    (d) Central tendency

    (e) Dispersion.

    (1 mark)

    52.If a function is defined such as y = f(x) = 5x + 4, then the inverse function

    1f (y) is

    (a) (y 5) / 4

    (b) (y 4) / 5

    (c) 5y + 4

    (d) 4y + 5(e) 4y 5.

    (1 mark)

    53.Find the harmonic mean of the following data:

    xi 3 4 5 6 7 8 9 10

    fi 2 3 10 12 17 7 4 2

    (a) 3.2555

    (b) 4.8265(c) 5.7565

    (d) 6.0865

    (e) 7.4545.

    (2 marks)

    54.Which of the following is true with regard to the simplex method of solving linear programming problems?

    (a) This method cannot be applied for solving problems involving two decision variables

    (b) At the optimal solution all the decision variables assume zero values

    (c) Slack variables are used to convert greater than or equal to type constraints into equations

    (d) At the optimal solution all the slack variables assume zero values(e) The Zj Cj value at the bottom of the solution column shows the value of the objective function for any

    solution.

    (1 mark)

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    55.The following data pertains to the consumption of materials by a bakery:

    Price

    (in Rs.)

    Quantities Used

    (Units)Inputs Units

    2005 2006 2005 2006

    Flour Kilogram 15 30 500 700

    Eggs Dozen 8 14 100 70

    Milk Litres 6 17 200 120

    Sugar Kilogram 10 16 50 70

    Laspeyres quantity Index for the year 2006 with the year 2005 as base year, is

    (a) 120.4

    (b) 124.8

    (c) 198.2

    (d) 206.0

    (e) 210.1.

    (1 mark)

    56.Consider the following information:

    2005 2006

    Commodity Price (in

    Rs.)

    Quantity

    (Kg)

    Price (in

    Rs.)

    Quantity

    (Kg)

    Wheat 7.50 5000 10.25 4800

    Rice 10.00 6000 14.00 5500

    Pulses 25.00 3000 28.00 3500

    Sugar 10.60 3000 14.50 2400

    Salt 2.60 500 4.50 600

    What is Fishers ideal price index for the year 2006 considering the year 2005 as the base year?

    (a) 112.82

    (b) 113.55

    (c) 127.35(d) 128.12

    (e) 133.58.

    (2 marks)

    57.Which of the following tests is/are not satisfied by Fishers ideal index?

    I. Factor reversal test.

    II. Time reversal test.III. Circular test.

    (a) Only (I) above

    (b) Only (II) above(c) Only (III) above

    (d) Both (I) and (II) above(e) Both (II) and (III) above.

    (1 mark)

    58.Which of the following price indices has a downward bias?

    (a) Laspeyres price index

    (b) Fishers ideal price index

    (c) Marshall-Edgeworth price index

    (d) Paasches price index

    (e) Laspeyres quantity index.

    (1 mark)

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    59.Using the linear trend relationship between sales and year estimated by the method of least squares from the data

    given below, predict the sales for the year 2005.

    Year 1999 2000 2001 2002 2003

    Sales of TV sets

    (in 000 units)12 18 20 23 27

    (a) 34,000 units(b) 35,300 units

    (c) 36,400 units

    (d) 37,500 units

    (e) 38,600 units.

    (2 marks)

    60.The estimated value of a variable according to the trend equation is 84.5 in a particular year and the actual value

    of the variable is 86.4. The relative cyclical residual is

    (a) 0.84

    (b) 1.16

    (c) 1.54

    (d) 1.96

    (e) 2.25.

    (1 mark)

    61.The marks obtained by 10 students in a semester examination in statistics are

    80, 83, 68, 86, 75, 73, 70, 70, 70 and 65.

    What is the mean absolute deviation?

    (a) 6.6

    (b) 5.6

    (c) 2.6

    (d) 7.5

    (e) 5.5.

    (1 mark)

    62.If

    2n 1

    n 1P+

    :2n 1

    nP

    = 3 : 5, then the value of n is

    (a) 2

    (b) 3

    (c) 4

    (d) 5

    (e) 6.

    (2 marks)

    63.The number of permutations of the word ACCOUNTANT,taking all the letters at a time is

    (a) 2,20,860(b) 2,26,800

    (c) 2,06,280(d) 2,08,600

    (e) 2,86,200.

    (1 mark)

    64.A committee of 3 ladies and 4 gentlemen is to be formed from a group of 8 ladies and 7 gentlemen. In how many

    ways can the committee be formed if one lady and one gentleman refuse to join?

    (a) 120

    (b) 800

    (c) 420

    (d) 1,540(e) 1,960.

    (2 marks)

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    65.In the following linear programming problem,

    Max. Z = 3x1 + 2x2 + 5x3

    Subject to constraints

    x1 + 2x2 + x3 < 430

    3x1 + 2x3 < 460

    x1 + 4x2 < 420x1, x2, x3 > 0.

    What is the maximum value of Z?

    (a) 890

    (b) 1,050

    (c) 1,110

    (d) 1,220

    (e) 1,350.

    (3 marks)

    66.In a linear programming problem, the feasible region is bounded by the following system of inequalities:

    2x +y 12 x +3y 21 x, y 0 Which of the following points is not a part of the feasible region?

    (a) (6, 0)

    (b) (0, 7)(c) (3, 6)

    (d) (4, 5)(e) (0, 0).

    (2 marks)

    67.The Arithmetic Mean (A.M) of two numbers exceeds their Geometric Mean (G.M) by 15 and Harmonic Mean

    (H.M) by 27. The lowest of the two numbers is

    (a) 20

    (b) 25

    (c) 30

    (d) 40

    (e) 50.

    (2 marks)

    68.In a survey of 100 readers, it was found that 50 read magazine A, 30 read magazine B and 15 read both the

    magazines. What is the probability of finding a person in the group who reads neither magazine A nor magazineB?

    (a) 0.15

    (b) 0.35(c) 0.65

    (d) 0.80

    (e) 0.85.

    (1 mark)

    69.The skewness of distribution is indicated by

    (a) Histogram

    (b) Ogive

    (c) Frequency polygon

    (d) Cumulative frequency table

    (e) Cumulative frequency curve.

    (1 mark)

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    70.The standard deviation of the first n natural numbers is

    (a)2n 1

    12

    (b)2n 1

    2

    (c) n 1

    12

    (d) n 1

    12

    +

    (e)3n 1

    12

    .

    (1 mark)

    71.

    If( )28 2 3

    1log log log x 4x 85 =

    3 +

    , then x =

    (a) 5(b) 4

    (c) 3

    (d) 2

    (e) 1.

    (1 mark)

    72.

    If

    2 2 2log x log y log z= =2 3 3k and

    3 2x y z 1= , then k =

    (a) 4(b) 2(c) 2

    (d) 4(e) 3.

    (2 marks)

    73.Linear programming cannot be used in

    (a) Selection of a product mix

    (b) Determination of a capital budget

    (c) Choice of mix of a short-term financing

    (d) Determination of Net Present Value (NPV) of a project

    (e) Problems where constraints are linear.

    (1 mark)

    74.In which of the following conditions a type I error is said to have occurred, in testing of hypothesis?(a) The sample statistic is incorrectly calculated

    (b) The sample variance is incorrectly calculated

    (c) Null hypothesis is rejected though it is true

    (d) Null hypothesis is accepted though it is false

    (e) The sample size is small.

    (1 mark)

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    75.In a control chart there are some observations that lie outside the upper and lower control limits. These points are

    referred as

    (a) Outliers(b) Attributes

    (c) Inherent variation

    (d) Assignable variation

    (e) Common variation.(1 mark)

    76.The demand for a particular product in a factory was observed to vary for every two months in a year. In a

    sample study, the following information was obtained:

    Month Jan March May July Sep Nov

    Products demanded 950 945 950 955 965 959

    The value of the2 -statistic from the given data is

    (a) 0.1358

    (b) 0.2725

    (c) 0.3645

    (d) 0.4658

    (e) 0.5642.

    (2 marks)

    77.The average cost of flats in Kolkata is Rs.7,00,000 with a standard deviation of Rs.60,000. What is the

    probability that a flat in Kolkata costs at least Rs.7,36,000? (Assume that cost of flats follow a normaldistribution.)

    (a) 0.3085

    (b) 0.2563

    (c) 0.3550

    (d) 0.2742

    (e) 0.3265.

    (1 mark)

    78.If the degrees of freedom increases

    (a) The normal distribution approaches t-distribution(b) The t-distribution approaches binomial distribution

    (c) Binomial distribution approaches F-distribution

    (d) F-distribution approaches t-distribution

    (e) t-distribution approaches normal distribution.

    (1 mark)

    79.In a test involving ANOVA the following details are obtained:

    Estimated population variance based on the variance among the sample means = 20

    Estimated population variance based on the variances within the samples = 14.77The F-ratio for the above data is

    (a) 0.739

    (b) 1.354

    (c) 5.230

    (d) 34.770

    (e) 295.400.

    (1 mark)

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    Suggested AnswersQuantitative Methods (CFA530): October 2007

    1. Answer : (e)

    Reason : In financial analysis extrapolation is widely used for :

    I. Forecasting future sales, cost and profit.

    II. Long-term capital requirements.

    III. Production of financial statements for financial institutions, banks, etc.

    All statements are true. Hence, option (e) is correct.