Federal Public Service Commission (FPSC) Competitive Examination for Recruitment to BPS-17 Posts under the Federal Government
Time Allowed: 3 Hours
PAPER: STATISTICS
MAXIMUM MARKS: 100 Marks
Attempt FIVE questions in all, including Question No.8 which is COMPULSORY. All questions carry EQUAL marks.
1. a) Write the applications of probability theory in decision making. (10) b) A study of credit card fraud was conducted by a crime researcher. According to collected data, it was found that 243 cases were of stolen cards, 85 of counterfeit card, 52 of mail orders and 46 of both stolen card and mail orders. Find the probability that a randomly selected case: (i) belongs to counterfeit card (ii) belongs to stolen card or mail order fraud (10)
2. a) According to the Labour Department, 15% of adult workers have a vocational diploma but they did not attend any institution. If 8 adults are randomly selected find the probability that: (i) at least half of them have diploma but they did not attend any institution. (ii) there is no such case that the adult has diploma but he did not attend any institution. (10) b) The serum cholesterol levels in men aged 18-24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7 (all units are in mg/100ml). If a man aged 21 is selected at random, find the probability that his serum cholesterol level is between 100 and 200. Find the probability that for a sample of 10 men aged 21-24 will have average serum cholesterol level greater than 200. (10)
3. a) Differentiate between: (i) One-tailed test and two-tailed test (ii) Interval and point estimation (iii) Simple and composite hypotheses (10) b) In an insurance study of pedestrian deaths in a country, monthly fatalities are analyzed for two different time periods. Sample data from the both time periods are summarized by the following statistics: n₁ = 12, x̄₁ = 46.42, s₁ = 11.07; n₂ = 15, x̄₂ = 51.06, s₂ = 10.39 At 0.05 level of significance, test the claim that both time periods have the same mean. (10)
4. a) What is the difference between a correlation problem and a regression problem? Also give the situation where we have to use partial correlation rather than simple correlation. (10) b) Randomly selected subjects ride a bicycle at 5.5 mi/h for one minute. Their weights (in pounds) are given with the number of calories used. Find the correlation coefficient between the both quantities.
Weights
167
191
112
129
140
173
119
Calories Used
4.23
4.69
3.21
3.47
3.72
4.45
3.36
(10)
5. a) When do we use Stratified Random Sampling? Write a general procedure to draw a stratified random sample. Also differentiate between stratum and cluster. (10)
b) What do you understand by sampling distribution? For a population of with elements 2, 4, 6, 8, 10, draw all possible random sample of size 2 without replacement and compute sample means. (10)
6. a) What are the applications of Statistics in daily life problems? (10) b) A drug supplying pharmaceutical company is administered to 3 patients, and the random variable X represents the number of cures that occur. The probabilities corresponding to 0 cure, 1 cure, 2 cures, and 3 cures are found to be 0.125, 0.375, 0.375 and 0.125 respectively. Find the expected value of X and its variance. (10)
7. Write short note on the following: (20) a) Poisson distribution b) ANOVA c) Coefficient of determination d) Systematic sampling
COMPULSORY QUESTION
8. (A) Write only the most appropriate option in your Answer Book, about the following statements. Do not reproduce the question. Cutting or overwriting is not allowed. (10)
(1) Which of the following is NOT a measure of central tendency? a) Median b) Mode c) G.M. d) Range
(2) A boarder security patrol that checks every passing vehicle, is using a) Complete enumeration b) Simple random sampling c) Systematic sampling d) Stratified sampling
(3) In binomial distribution a) mean > variance b) mean < variance c) mean = variance d) mean ≤ variance
(4) For regression line, Y = 2 − 5X a) The Y-intercept is 2 b) The Y-intercept is -5 c) The slope of line is -5 d) both (a) & (c)
(5) Any set of outcomes of a random experiments is called a) event b) sample points c) random variable d) event space
(6) A complete program to take sample, is called a) stratum size b) unit list c) sampling frame d) sample design
(7) Which is NOT the property of a point estimator? a) Unbiasedness b) Consistency c) Accuracy d) Sufficiency
(8) If one event is unaffected by the outcome of another event, the two events are said to be a) Independent b) Mutually exclusive c) Dependent d) All (a), (b), & (c)
b) What do you understand by sampling distribution? For a population of with elements 2, 4, 6, 8, 10, draw all possible random sample of size 2 without replacement and compute sample means. (10)
6. a) What are the applications of Statistics in daily life problems? (10) b) A drug supplying pharmaceutical company is administered to 3 patients, and the random variable X represents the number of cures that occur. The probabilities corresponding to 0 cure, 1 cure, 2 cures, and 3 cures are found to be 0.125, 0.375, 0.375 and 0.125 respectively. Find the expected value of X and its variance. (10)
7. Write short note on the following: (20) a) Poisson distribution b) ANOVA c) Coefficient of determination d) Systematic sampling
COMPULSORY QUESTION
8. (A) Write only the most appropriate option in your Answer Book, about the following statements. Do not reproduce the question. Cutting or overwriting is not allowed. (10)
(1) Which of the following is NOT a measure of central tendency? a) Median b) Mode c) G.M. d) Range
(2) A boarder security patrol that checks every passing vehicle, is using a) Complete enumeration b) Simple random sampling c) Systematic sampling d) Stratified sampling
(3) In binomial distribution a) mean > variance b) mean < variance c) mean = variance d) mean ≤ variance
(4) For regression line, Y = 2 − 5X a) The Y-intercept is 2 b) The Y-intercept is -5 c) The slope of line is -5 d) both (a) & (c)
(5) Any set of outcomes of a random experiments is called a) event b) sample points c) random variable d) event space
(6) A complete program to take sample, is called a) stratum size b) unit list c) sampling frame d) sample design
(7) Which is NOT the property of a point estimator? a) Unbiasedness b) Consistency c) Accuracy d) Sufficiency
(8) If one event is unaffected by the outcome of another event, the two events are said to be a) Independent b) Mutually exclusive c) Dependent d) All (a), (b), & (c)
