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Wednesday 29 December 2010

CSS Paper Of STATISTICS 2010

STATISTICS
FEDERAL PUBLIC SERVICE COMMISSION
COMPETITIVE EXAMINATION FOR
RECRUITMENT TO POSTS IN BPS-17 UNDER
THE FEDERAL GOVERNMENT, 2010
STATISTICS


(PART-I) 30 MINUTES MAXIMUM MARKS:20
TIME ALLOWED:
(PART-II) 2 HOURS & 30 MINUTES MAXIMUM MARKS:80
PART – I (MCQs)
(COMPULSORY)

Q.1. Select the best option/answer and fill in the appropriate box on the Answer Sheet. (20)
(i) Four coins are tossed simultaneously, in how many distinct ways these coin can show up?
(a) 8 (b) 4 (c) 16 (d) 32 (e) None of these
(ii) In how many ways five people can fill five distinct posts?
(a) 60 (b) 120 (c) 25 (d) 50 (e) None of these
(iii) Let X be a random variable distributed like Binomial with n=10 and p=0.345, then what will be
E(X)?
(a) 34.5 (b) 3.45 (c) 0.0345 (d) None of these
(iv) What is P(A B) equals to, when A and B are mutually exclusive events?
(a) P(A)+P(B) (b) P(A) x P(B) (c) P(A)+P(B)-P(AB) (d) None of these
(v) What is P(A B) equals to when A and B are two independent events?
(a) P(A)+P(B) (b) P(A) x P(B) (c) P(A)+P(B)-P(AB) (d) None of these
(vi) For which probability distribution function mean and variance are equal?
(a) Normal (b) Binomial (c) Poisson (d) Gamma (e) None of these
 (vii) How many ways all possible distinct committees of 3 students can be formed from a class of 10
students?
(a) 30 (b) 120 (c) 125 (d) 720 (e) None of these
(viii) Let Y be a random variable distributed like Binomial with n=5 and p=0.70, then what will be the
variance of Y?
(a) 0.105 (b) (0.105)2 (c) 3.5 (d) 0.14 (e) None of these
(ix) Let Y= α + β X + error. What β is called?
(a) mean of X (b) Y-intercept (c) slope (d) variance of Y (e) None of these
(x) If the standard deviation of a random variable X is 5, then what will be the standard deviation of
Y=4x+2?
(a) 400 (b) 20 (c) 22 (d) 402 (e) None of these
(xi) A question was asked, whose answer is either YES or NO, to 150 individuals from a section of
population, of them 90 gave YES answer. What will be the value of Chi-square if the hypothesis
to be tested is P(YES)=P(NO)?
(a) 5 (b) 6 (c) 15 (d) 25 (e) None of these
 (xii) What does the probability of “rejecting null hypothesis when it is true’’ called?
(a) Type-I error (b) Type-II error (c) Level of confidence
(d) Least error (e) None of these
NOTE: (i) First attempt PART-I (MCQ) on separate Answer Sheet which shall be taken back after
30 minutes.
(ii) Overwriting/cutting of the options/answers will not be given credit.
(iii) Statistical Table will be provided if requested.
 (iv) Use of Scientific Calculator is allowed.
Roll Number
STATISTICS

 (xiii) Let x1, x2, …, xn be a random sample from N(μ,σ2). What is the sampling distribution of
S n
X
/
( )
_
?
(a) F-distribution (b) Normal distribution (c) Z-distribution
(d) t-distribution (e) None of these
(xiv) A researcher wishes to draw sample of individuals from poor, middle and rich economic class.
Which type of sampling method is appropriate?
(a) Simple random sampling (b) Stratified sampling (c) Systematic sampling
(d) convenient sampling (e) None of these
(xv) What test statistics is used in the Analysis of variance?
(a) F-statistics (b) T-statistics (c) Chi-square statistics
(d) Z-statistics (e) None of these
 (xvi) What is the sampling distribution of sample mean if the random sample of size n=50000 is drawn
form a Poisson distribution?
(a) Normal distribution (b) Standard normal distribution (c) T-distribution
(d) F-distribution (e) None of these
(xvii) How many distinct all possible random samples, with replacement, each of size n=3 can be drawn
from a finite population of size N=50?
(a) 125000 (b) 19000 (c) 750 (d) 127500 (e) None of these
(xviii) P(A/B)=? When A and B are non-independent events.
(a) P(A) /P(B) (b) P(B) + P(B) (c) P(AB) P(B) (d) P(AB)/P(B) (e) None of these
(xix) To test the hypothesis H0 : μ1 = μ2 = … =μk one can apply:
(a) Analysis variance (b) Regression analysis (c) Analysis mean
(d) t-test (e) None of these
(xx) What is the range of coefficient of determination R2 ?
(a) (-1, 1) (b) (0,1) (c) (0, ∞) (d) (- ∞, ∞) (e) None of these
PART – II

NOTE:
(i) PART-II is to be attempted on the separate Answer Book.
(ii) Attempt ONLY FOUR questions from PART-II. All questions carry EQUAL marks.
(iii) Extra attempt of any question or any part of the attempted question will not be
considered.
Q.2. In a small town only three news papers, A, B, and C, are available for the readers. Suppose that
60% of the readers subscribe to newspaper A, that 40% subscribe to newspaper B, and that 30%
to newspaper C. Suppose also that 20% of them subscribe to both A and B, that 10% subscribe
to both A and C, that 20% subscribe to both B and C, and that 5% subscribe to all three
newspapers.
(a) Construct Venn diagram to present the above situation. (8)
(b) What percentage of newspaper readers subscribe at least one of the three newspapers? (8)
(c) What percentage of newspaper readers subscribe none of the three newspapers? (4)
Q.3. Suppose that in a certain drug the concentration of a particular chemical is a random variable
with the following continuous distribution:
g(x)= (3/8)x2 for 0 ≤ x ≤ 2 & 0 elsewhere.
Suppose that the concentrations X and Y of the chemical in two separate batches of the drug are
independent random variables each with the same p.d.f g. Determine:
(a) the joint p.d.f of X & Y (6)
(b) P( X > Y) (6)
(c) P( X+Y ≤ 1) (8)
Q.4. Let X be Binomial random variable with parameters “n” and “p”. Find mean and variance
(a) by expectation method (10)
(b) Using moment generating function (10)
STATISTICS

Q.5. (a) Describe and explain the principal of least square. Also find the least square estimates of linear
regression model. (8)
(b) A study was conducted on the amount of converted sugar (Y) in a certain process at various
temperature (X). The data were recorded as follows:
Fit linear regression model of Y on X . Also estimate the amount of converted sugar produced
when the coded temperature is 1.78. Comment on the result. (12)
Q.6. (a) To study the relationship between eye and hand literality, the data on 413 subject were
presented in the following table:
Test, at 5% of level of significance, the hypothesis that eye and hand literalities are independent.
Also compute the coefficient of contingency. Comment. (12)
(b) In 180 throws of a die the observed frequency of the values 1 to 6 are 34, 27, 41, 18, 35. By
using appropriate testing method, test whether the die is unbiased. (Use α=.05) (8)
Q.7. (a) An antipyretic is being tested as a replacement for aspirin. A total of nine experimental animals
are given artificially high temperature and the drug is administered. Given before and after
temperatures, test the hypothesis that the drug is effective; use the 0.05 level of significance. (8)
(b) Two independent random samples of sizes 60 and 72 have means and standard deviations,
respectively, 112.6, 1
x 24.8, 1 s 103.9, 2
x 19.7, 1 s test the hypothesis that μ1 = μ2 at
α=.05 and construct a 95% confidence interval for μ1 - μ2. (12)
Q.8. Write brief notes on ANY FOUR of the following: (5+5+5+5)
(i) The relationship between regression and correlation.
(ii) Latin Square Design.
(iii) Conditional Probability.
(iv) Use of Statistics in social science.
(v) Mathematical expectation.
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