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Old Wednesday, October 10, 2007
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Default Statistics Paper 2007

FEDERAL PUBLIC SERVICE COMMISSION
COMPETITIVE EXAMINATION FOR RECRUITMENT TO POSTS
IN BPS – 17 UNDER THE FEDERAL GOVERNMENT, 2007.

STATISTICS

TIME ALLOWED: THREE HOURS MAXIMUM MARKS:100

NOTE: (i) Attempt FIVE questions in all including question No. 8 which is compulsory. All questions carry EQUAL marks.
(ii) Extra attempt of any question or any part of the attempted question will not be considered
(iii) Candidate must draw two straight lines (==================) at the end to separate each question attempted in Answer Books.

Q.1. (a) Give different approaches to define probability. (5)
(b) In a small city, two news papers A and B are published. The circulation departments report that 22% of the city’s househo lds have a subscription to A while 35% subscribe to B. A survey reveals that 6% of all households subscribe to both newspapers. What proportion of the households subscribe to at least one newspaper? (7)
(c) Three airlines A, B and C serve for a city. Airline A has 50% of all the scheduled flights, B has 30%, and airline C has the remaining 20%. Their on-time rates are 80%, 65% and 40% respectively. A plane has just left on time. What is the probability that it was airline B? (8)

Q.2. (a) Most of internet service providers (ISPs) attempt to provide a large enough service so that customers seldom encounter a busy signal. Suppose that the customers of one ISP encounters busy signals 8% of the times. Suppose, during a week a customer of this ISP called 12 times. What is the probability that he did not encounter any busy signals? What is the probability that he did not make internet connection in his all 12 tries? (10)
(b) Prove that for Poisson distribution, means and variance are equal. (10)

Q.3. (a) What is Statistical Inference? Also explain the properties of a good point estimator. (10)
(b) Suppose that average marks (out of 10) of 35 randomly selected candidates appeared in an interview for civil services, are 5.6 The marks are normally distributed with a standard deviation of 2. Calculate 95% confidence interval for mean marks of all the candidates. (5)
(c) Write general procedure for testing a hypothesis of means of a population. (5)

Q.4. (a) In order to check the performance of city government a survey was conducted whether or not people are satisfied with the city government. A random sample of 1250 person was taken and 680 responded in “Yes”. At 10% level of significance, test whether the survey’s result was in the favour of the government? (8)
(b) Suppose, we want to compare the mean protein intake of all people with income below the poverty level to that of all people with incomes above the poverty level. The data given below display the protein intakes; in grams, of a 24-hours period for independent random samples of 10 people with income below the poverty level and 8 people with income above the poverty level. (12)

Below poverty level: 51.4 76.7 73.7 66.2 65.5 49.7 65.8 62.1 75.8 62.0
Above poverty level: 86.0 59.7 68.6 98.6 87.7 69.0 80.2 78.1

Do the data provide sufficient evidence to conclude that the mean protein intake of the people with above poverty level is higher than those with below poverty level? (Use 5% level of significance)

Q.5. (a) The general manager of an engineering firm wants to know whether a draftsman’s experience influences the quality of his work? He selects 10
draftsmen at random and records their years of work experiences and their wOrk quality rating (excellent = 5, very good = 4, good = 3, average = 2, and poor = 1). The data recorded are given as follows: (10)

Experience: 1 17 20 9 2 13 9 23 7 10
Rating: 1 4 4 5 2 4 3 5 2 5

Find correlation coefficient between experience and rating. Also interpret
The result.
(b) For the following data of Annual Expenditure (in Rs. Millions, X) for R & D and Annual Profit (in Rs. Millions, Y) of firm, estimate the regression equation.(10)
Y: 31 40 34 30 25 20
X: 5 11 5 4 3 2

Q.6. (a) What are the main advantages of sampling? Give at least one example where sampling is inevitable. Also give a situation where stratified ransom sampling should be sued rather simple random sampling. (10)
(b) What are the applications of Statistics in Socio-economic problems of community? (10)

Q.7. Write short note on the following: (5 each)
(a) Applications of Normal Distribution
(b) Type-I and Type-II Errors
(c) Partial and Multiple Correlation
(d) Cluster Sampling

COMPULSORY QUESTION

Q.8.(A) Write only the correct answer in the Answer Book. Do not reproduce the question.

(1) A cricket captain wins the toss for three consecutive matches. What is the probability that the will call correctly for the fourth match?
(a) 1/16
(b) 1/8
(c) 1/4
(d) 1/2
(e) None of these

(2) A and B are two independent events. The probability of A is Ľ and B is 1/3. The neither probability of A nor B is:
(a) 5/12
(b) 1/3
(c) 3/4
(d) 11/12
(e) None of these

(3) Which one of the following statement is not true?
(a) Mutually exclusive events are statistically dependent.
(b) Complementary events have probabilities that sum to 1.
(c) Opposite events, are statistically independent.
(d) An experiment’s elementary events are collectively exhaustive and mutually exclusive.
(e) None of these

(4) For a Poisson distribution with standard deviation equals to 2 then mean of the Poisson distribution equals to:
(a) 0
(b) 1
(c) 2
(d) 4
(e) None of these

(5) Which of the following could never by described by the binomial distribution?
(a) The number of defective items produced by an assembly process.
(b) The amount of water used daily by a single household.
(c) The number of people in a class who can answer a particular question
correctly.
(d) All of these
(e) None of these

(6) The area under the normal curve within two standard deviation of the mean is:
(a) 68.26 %
(b) 95.44 %
(c) 99.73 %
(d) 99.99 %
(e) None of these

(7) What information is given by a value of the coefficient of determination?
(a) Strength of relationship
(b) Both strength and direction of relationship
(c) Neither strength nor direction of relationship
(d) Direction of relationship only
(e) None of these

(8) A complete list of all the sampling units is called:
(a) stratum size
(b) unit list
(c) sampling frame
(d) sample design
(e) None of these

(9) If we decrease Type-I error, Type-II error:
(a) Remains same
(b) Increases
(c) Decreases
(d) None of these

(10) To test of equality of means of paired observations, we use:
(a) Chi-Square test
(b) t-test
(c) F-test
(d) Z-test
(e) None of these

Q.8.(B) Write only “T” for “True” or “F” for “False” in the Answer Book. Do not reproduce the question
.

(1) Extreme values in a data set have a strong effect on the median. T/F
(2) In symmetrical distribution, the means, median, and mode are equal;
provided that the mode is a single number. T/F
(3) Joint events are those that are not mutually exclusive. T/F
(4) Classical probability assumes that each of the possible outcomes of
an experiment has equal chance to exist. T/F
(5) The mean of t-distribution is zero. T/F
(6) There is no difference between random error and sampling bias. T/F
(7) To perform a complete enumeration, one would need to examine every item in a population. T/F
(8) A consistent estimator is one that tends to be more accurate with large
samples than with small ones. T/F
(9) The type-II error is equivalent to rejecting the alternative hypothesis when it is true. T/F
(10) An upper-tailed test occurs when H
o : µ ł µo and H1 : µ < µo . T/F
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