CSS Statistics Past Paper 2017

Instructions specific to this paper

• Attempt ONLY FOUR questions from PART-II by selecting TWO questions from EACH
• Use of Calculator is allowed.
• Co-efficient of Skewness and discuss the result from the following weekly
• pr{ 2} (ii) 1+ 2 (iii) 1 2 3
• pr{ + } (v) pr{ 3|E1 2} (vi) pr{ + 2 }

Questions

1. Q. 28 marks

   (a) Suppose a set of observations has mean and variance s2. What happens to the mean and variance if each score is divided by s and then is subtracted from each quotient? Is the result same if you first subtract from each score and then divide the difference by s? (b) Calculate ( i) S. D ( ii) Co-efficient of variation (12) (iii) Co-efficient of Skewness and discuss the result from the following weekly wages of 300 workers. Below Below Below Below Below Below Below Weekly wages 5 10 15 20 25 30 35 No. of workers 7 78 120 189 205 275 300

2. Q. 38 marks

   (a) If the probability that an individual suffers a bad reaction of a given serum is 0.001, determine the probability that out of 2000 individuals (a) exactly 3 and (b) more than 2 individuals will suffer a bad reaction. Find the answer using both poisson and the binomial distributions. (b) A random variable to assume the value 1 with probability p, with probability (6) q = 1 - p. Prove that (a) E(X) = p and (b) E[(X - )2] = pq. (c) An experiment consists of drawing three cards in succession from a well- (6) shuffled ordinary deck of cards. Let be the event “king” on the first draw, be the event “king” on the second draw, be the event “king” on the third draw. State in words the meaning of each of the following: (i) pr{ 2} (ii) 1+ 2 (iii) 1 2 3 (iv) pr{ + } (v) pr{ 3|E1 2} (vi) pr{ + 2 }

3. Q. 48 marks

   (a) What is regression model? Write the assumptions made in a linear regression. Also proof the Comment on the unbiasedness of regression estimates. (b) Calculate coefficient of correlation by the method of least squares for the (12) following paired values of X and Y variables. Also verify that this value of r is same as that obtained by pearson’s formula. X 10 12 13 17 18 Y 5 6 7 9 13 STATISTICS

4. Q. 58 marks

   (a) Discuss time reversal test and explain the factor reversal test. (b) Per capita income of a person from 1980-81 to 1986-87 and the consumer price (12) index with 1980-81 were as follows: Income per Year Index Nos. capita (Rs) 1980-81 1627 100 1981-82 1851 103.5 1982-83 1993 103.4 1983-84 2290 109.4 1984-85 2494 110.9 1985-86 2735 113.8 1986-87 2970 115.6 Find real wages and real income indices.

5. Q. 68 marks

   (a) What is the difference between population census and vital statistics? What are the various uses of vital statistics for a country? (12) (b) The population and its distribution by sex and number of births in a tehsil in 1991 and survival rates are given below: Group Population Males Females Male Female Total Survival rate birth birth birth 15-19 11832 6145 5687 65 60 125 0.91 20-24 10538 5214 5324 144 132 276 0.90 25-29 9375 4655 4720 135 127 262 0.84 30-34 7843 3910 3933 82 81 163 0.87 35-39 7270 3600 3670 62 56 118 0.85 40-44 6315 3290 3025 12 15 27 0.83 45-49 5394 2793 2601 3 3 6 0.82 Total 58567 29607 28960 503 474 977 From the given data, calculate (i) General fertility rate (ii) Age specific fertility rate (iii) Total fertility rate (iv) Gross production rate (v) Net reproduction rate Assuming no mortality.

6. Q. 78 marks

   (a) Given the following data obtained from a completely randomized design with four treatments; analyse the given data and draw conclusion about the equality of treatment effects. Treatments T1 T2 T3 T4 20.9 5.8 23.7 13.2 12.4 6.1 14.4 10.2 10.1 4.8 9.0 5.1 4.2 1.5 (b) Give Statistical model for completely randomized design with one observation per unit. (6) (c) What is the role of randomization in the process of the experimentation? (6) Discuss and define experimental error. What factors are responsible for determining the number of replications? STATISTICS

7. Q. 88 marks

   (a) A random sample of 100 workers in a farm took an average of 14 minutes to complete a task. A random sample of 150 workers in another large farm took an average of 11 minutes to complete the task. Can it be assumed at 1% level of significance that the average time taken by the workers in the two farms is same, if the S.D. of the workers of first farm and second farm are 2 minutes and 3 minutes respectively? (b) Describe the general procedure for testing a hypothesis about a difference (6) between population mean, when sample size is large. (c) Distinguish between: (6) (i) Sampling error and non-sampling error (ii) Sampling with replacement and without replacement (iii) Probability and non-probability Sampling

Standard FPSC instructions

Printed on this and every CSS paper.

• Part-II is to be attempted on the separate Answer Book.
• All the parts (if any) of each question must be attempted at one place instead of at different places.
• Write Q. No. in the Answer Book in accordance with Q. No. in the question paper.
• No page/space be left blank between the answers. All the blank pages of the Answer Book must be crossed.
• Extra attempt of any question or any part of the attempted question will not be considered.