M.Sc. (Semester II) (CBCS) Examination, 2017
STATISTICS
STATISTICAL METHODS
Day Date: Friday, 28-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
N.B. Attempt five questions.
Q no. 1 Q. no. 2 are compulsory.
Attempt any three questions from Q. no. 3 to Q. no. 7
Figures to the right indicate full marks.
Non-programmable /simple calculator is allowed.
Q.1 Choose the correct Answer: 10
If 25% of the items are less than 30 and 25% items are more
than 70 then quartile deviation is
20 30 40 50
To compare consistency of observations among two data
sets, we can use as most efficient measure of
dispersion.
rang mean deviation
quartile deviation coefficient of variation
If two regression coefficients are
and then correlation
coefficient r is




The range of Spearman's rank correlation is
to to 1 0 to 1 0 to
If correlation coefficient between X and Y is 0.8 then the
correlation coefficient between and is
0.4 0.8 0.4 0.64
If a constant value 20 is subtracted from each observation of
a set, then arithmetic mean of set is
non affected increased by 20
decreased by 20 20 times the original value
If the arithmetic mean of two observation is 6.5 and
geometric mean is 6 then two observation
6 5 6 9
Page 2 of 3
If a perfect coin is tossed twice then probability of getting
both the head is




If X follows binomial distribution with parameters n and p
then
mean variance mean variance
mean variance none of these
10) For testing simple hypothesis against a simple alternative,
which of the following values of and is not correct?
and and
and and
State whether true or false. 04
For Bernoulli distribution mean is always less than variance.
Nonparametric test does not make any assumption
regarding the form of the population.
For normal distribution, mean median mode.
Rejecting null hypothesis when it is actually true is the type II
error.
Q.2 Answer the following: 06
Define the terms Arithmetic mean, Median and mode.
If X has Poisson distribution such that 2P
Find mean and variance.
Write short notes on following. 08
Addition and Multiplication rules of probability
Run test
Q.3 What is dispersion? 07
Define Standard deviation
Quartile deviation
Coefficient of variation
The marks of 25 students are given below.
Marks 0-10 10-20 20-30 30-40 40-50
students 3 4 10 1
Calculate the missing frequency and hence obtain the values
of mean, median and mode.
07
Q.4 Define Karl Pearson's correlation coefficient and regression
coefficients. State the relation between correlation coefficient
and regression coefficients. If sign of one regression
coefficient is known, how will you decide the sign of correlation
coefficient and other regression coefficient?
07
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Following data gives price and demand of a commodity in 10
days.
07
Price 2 5 4 8 10 9 5 6 7 4
Demand 8 6 7 3 2 4 5 3 2 10
Find the Karl Pearson's coefficient of correlation between price
and demand and interpret the result.
Q.5 Define probability mass function of random variable X. A
discrete random variable X has the following probability
distribution.
X 0 1 2 3
0.1 k 0.2 2k 0.3 3k
Find the value of k.
Evaluate )and
07
Define binomial distribution with parameters n and p. If X is a
binomial variate with n=5 and p=0.3,
Find

07
Q.6 Define exponential distribution with parameter . Suppose
lifetime of automobile batteries is exponentially distributed with
mean 1000 days. What is the probability that such a battery
will last more than 1200 days?
07
Describe the sign test for testing that the population median is
M0 against the alternative that the median is M1 M0
07
Q.7 Describe a large sample test procedure for testing the
proportion P in the population has specified value P0. In a
hospital, 138 female and 162 male babies were born in a
week. At level of significance, does these figures confirm
to the hypothesis that male and female babies born in equal
proportion?
07
Following data shows the performance of two batsmen A and
B.
Batsman A Batsman B
Number if innings 50 40
Mean runs 55 50
Standard deviation 8 10
Which batsman is more consistent in score? Which batsman is
better in scoring the runs?