# Mock Test Stats2011

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

STATISTICAL METHODS IN ECONOMICS

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.
2

(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
Or

(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
why?

(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
Find
(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 .
3

(c)    Prove that two mutually exclusive events with positive probabilities
cannot be independent.                                             4
Or
(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
www.ecoblisspoint.com
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

Or
(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.
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
www.ecoblisspoint.com
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

Or

(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.
Calculate:
(i)     The regression coefficient byx;
(ii)    The standard error of the regression coefficient of Y on X
(SEb).

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

Bliss Point Studies                        3                                         Amit
9811343411                                                                     9891555578
www.ecoblisspoint.com
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
Or
(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
www.ecoblisspoint.com

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