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					B.A. (H) Economics I Year                                                    MOCK TEST


Time : 2 Hours                                              Maximum Marks : 38
           Attempt All questions. Use of simple calculator is allowed

1.    (a)    For the numbers (X) : 1, 3, 4, 5 and 12, find:

             (i) the value v  for which  X  v is minimized.

             (ii) the value v  for which  X  v is minimized.                            2

      (b)    The first four moments about 4 are 1, 3, 43 and 146. Is the data
             consistent? Explain.                                           2

      (a)    Given that mean of a distribution is 50 and mode is 58:                        2
             (i)    Calculate the median;
             (ii)   What can you say about the shape of the distribution? Explain

      (b)    Given that the mean of a distribution is 5, variance is 9 and the moment
             coefficient of skewness is –1, find the first three moments about the
             origin.                                                                2

2.    (a)    A random variable has the following probability distribution :
             Value of X  :      0     1       2     3
             Probability :      0.1   0.3     0.4   0.2
             (i) E(X) and (ii) Var (X)                                                      3

      (b)    If the random variable X is normally distributed with mean μ and
             variance σ 2 , derive the mean and variance of the variable z  X  μ /σ .

      (c)    Prove that two mutually exclusive events with positive probabilities
             cannot be independent.                                             4
      (a)    (i)    Write the axioms of probability.
             (ii)   What is the chance that a leap year selected at random will
                    contain 53 Sundays?                                      3

Bliss Point Studies                         1                                     Amit
9811343411                                                                  9891555578
B.A. (H) Economics I Year                                                  MOCK TEST

      (b)    The probability that a teacher will give an unannounced test during any
             class meeting is 1/5- If a student is absent twice, what is the probability
             that he will miss at least one test?                                      3

      (c)    In an examination a student passes if he secures 30% or more marks. He
             is placed in the first, second or third divisions accordingly as he secured
             60% or more marks, between 45% and 60% marks and between 30% and
             45% respectively. He gets a distinction in case he secures 80% or more
             marks. It is noticed from the results that 10% of the students failed
             whereas 5% of them obtained distinction. Calculate the percentage of
             students placed in the second division. (Assume marks to be normally
             distributed).                                                             4

3.    (a)    Differentiate between Type I and Type-II errors.                           2

      (b)    Show that sample variance is a consistent estimator but not an unbiased
             estimator of population variance. What would be an unbiased estimator
             of the population variance?                                           4
      (c)    A die is suspected of being biased. It is rolled 24 times with the following
             result. Conduct a significance test to see if it is biased :               4
             Outcome      Frequency
             1            8
             2            4
             3            1
             4            8
             5            3
             6            0

      (a)    An international airline analyzed the data on 200 randomly selected
             booking of seats according to the method used for making reservations
             and the class of travel. The results are presented below:
                                               Reservation Method
             Class of Travel          Travel Agent  Internet      Toll-free no.
             Business Class               18           11               9
             Economy Class                55           65              42
             Test at 5% level of significance the airline’s belief that class of travel is
             unrelated with the method used for reservations.                            4
      (b)    A population consists of the numbers 12, 14 and 16.
             (i)     Enumerate all possible samples of size two which can be drawn
                     from the population (without replacement).
             (ii)    Show that the mean of the sampling distribution of the sample
                     means is equal to the population mean.
             (iii)   Calculate the variance of the sampling distribution of the sample
                     mean and show that it is less than the population variance.     3

Bliss Point Studies                     2                                        Amit
9811343411                                                                 9891555578
B.A. (H) Economics I Year                                                       MOCK TEST

      (c)    (i)     Distinguish between a parameter and a statistic.
             (ii)    Derive the variance of the sampling distribution of the sample
                     mean. Is it more than population variance?                   3

4.    (a)    In regression analysis, the sum of squares of the deviations about the
             mean for the predicted scores is 80 and the sum of squares of the error is
             40, what is R 2 ? Explain.                                            3

      (b)    The rank correlation of physical fitness contest involving 12 participants
             was calculated as 0.6. However, it was later discovered that the
             difference in ranks of a participant was read as 8 instead of 3. Find the
             correct coefficient of rank correlation.                                3

      (c)    Given the regression line
             Y  2.27X  0.79, r 2  0.98, Sx  26.67, SY  17.68 , for 9 pairs of observations,
             calculate :
             (i)     Standard error of the regression of Y on X;
             (ii)    Standard error of the regression coefficient b y x ;

             (iii)   95% confidence interval for the population regression coefficient
                     βyx .                                                           4


      (a)    The equations of two regression lines between two variables are
             expressed as
             2X – 3Y = 0 and
             4Y – 5X – 8 = 0
             (i)     Identify which of the two can be called regression of Y on X and X
                     on Y.
             (ii)    Find the means of the variables.
             (iii)   Determine rXY .                                                          3

      (b)    The following results were obtained from a random sample of 50
             observations from a bivariate distribution: sx = 3.65, sy= 7.3 and rxy=0.6,
             where sx and sy are sample standard deviations and rxy is sample
             correlation coefficient between X and Y.
             (i)     The regression coefficient byx;
             (ii)    The standard error of the regression coefficient of Y on X

             (iii)   Test the hypothesis: β y x  0 .                                         4

Bliss Point Studies                        3                                         Amit
9811343411                                                                     9891555578
B.A. (H) Economics I Year                                               MOCK TEST

      (c)    What do you mean by the standard error of estimate of the linear
             regression of Y on X? If two variables are perfectly correlated, find the
             standard error of estimating Y from X.                                  3

5.    (a)    Show that in general, the Laspeyre’s Price Index is greater than the
             Paasche’s Index. When would this not be so?                       3

      (b)    Show that Laspeyre’s Price Index can be written as a weighted average of
             price relatives. What are the weights?                                1
      (a)    During a certain period the consumer price index increased from 110 to
             200 and the salary of a worker also increased from Rs. 3500 to Rs. 5000.
             What is the real gain, if any, to the worker?                         1

       (b)   A fresh graduate is offered jobs by a recruiting company in cities A and
             B. He is offered monthly salary of Rs. 20000 in A and Rs. 18000 in B.
             Given that the consumer price index is 180 in A and 150 in B.
             (i)    Which job offer should he accept?
             (ii)   How much should be the minimum salary at which he would
                    accept the other job offer?                          3


Bliss Point Studies                    4                                     Amit
9811343411                                                             9891555578

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