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FPSC · CSS 2024

Statistics

100 marks · 3 hours · 6 questions · official PDF, 3 pages
Practice 19 MCQs
This paper Statistics · all yearsQ. 2 · What methods you employed in…Q. 4 · An urn contains 10 white…Q. 5 · Find the sampling distribution of…Q. 6 · A confidence interval is constructed…Q. 7 · The prices and quantities of…Q. 8 · In a Randomized Complete Block…With this paperPart-I MCQs19Official PDF3 pp← 20232025 →
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Section A

Q. 2
  1. (a)What methods you employed in the collection of statistical data when the field of inquiry is (i) small, (ii) large and (iii) very large, if you are to pay due regard to accuracy, labor, cost and time. [10]
  2. (b)If log x is normally distributed with μ = 1 and σ² = 4, find P(1 <x < 2), given log₂ 0.693. [10]
(10)
Q. 4
  1. (a)An urn contains 10 white and 3 black balls. Another urn contains 2 white and 5 black balls. Two balls are transferred from first urn and placed in the second urn. Later a ball is taken from the latter. What is the probability that it is a white ball? [10]
  2. (b)Differentiate between Poisson distribution and Poisson process. Give examples in each case. [10]
(20)
Q. 5
  1. (a)Find the sampling distribution of the mean if a sample of three numbers is taken without replacement. How does the variance of the sampling distribution compare with the population variance? [10]
  2. (b)A random sample of size n = 100 is taken from a population having a mean of 20 and a standard deviation of 5. The shape of the population distribution is unknown. (i) What can you say about the sampling distribution of the sample mean? (ii) Find the probability that sample mean exceeds 20.75. [20]
(20)

Section B

Q. 6
  1. (a)A confidence interval is constructed from a random sample of size n = 50, for the mean yield of a normal population which has σ = 21 tons. The limits for the interval are 866.11 and 875.89 tons. What confidence co-efficient was used? [10]
  2. (b)How will you construct confidence interval for difference of means of a normal population? [10]
(20)
Q. 7

The prices and quantities of three commodities during 2002 and 2004 are given below: Commodity Prices (Rs. Per 40 Kilograms) Quantities Produced (Kgs.) 2002 2004 2002 2004 A 3.95 4.25 9,675 16,436 B 34.80 38.04 78 83 C 61.56 59.70 118 116 Compute the Marshall-Edgeworth and the Walsh's price index numbers for 2004, using 2002 as the base period.

  1. (a)Describe the main steps involved in the construction of index numbers of wholesale prices. [10]
  2. (b)The prices and quantities of three commodities during 2002 and 2004 are given below: Commodity Prices (Rs. Per 40 Kilograms) Quantities Produced (Kgs.) 2002 2004 2002 2004 A 3.95 4.25 9,675 16,436 B 34.80 38.04 78 83 C 61.56 59.70 118 116 Compute the Marshall-Edgeworth and the Walsh's price index numbers for 2004, using 2002 as the base period. [10]
(10)
Q. 8

In a Randomized Complete Block Design, in each of four blocks I, II, III, IV, four varieties of wheat A, B, C, D are grown in the layout given below and the yields are also indicated therein: Block Plot 1 Plot 2 Plot 3 Plot 4 I B 27 A 17 C 15 D 25 II A 28 D 22 B 26 C 16 III D 14 C 11 A 22 B 25 IV C 18 H 18 D 19 A 17 Note: Letters represent varieties (A, B, C, D) and numbers represent yields (i) Perform the analysis of variance to test at 0.05 significance level, the difference in the yields of varieties and in blocks. (ii) What would be the result if no blocking had been done, i.e., if we consider it as a completely randomized design?

  1. (a)Describe a Randomized Complete Block Design experiment and give its layout. [10]
  2. (b)In a Randomized Complete Block Design, in each of four blocks I, II, III, IV, four varieties of wheat A, B, C, D are grown in the layout given below and the yields are also indicated therein: Block Plot 1 Plot 2 Plot 3 Plot 4 I B 27 A 17 C 15 D 25 II A 28 D 22 B 26 C 16 III D 14 C 11 A 22 B 25 IV C 18 H 18 D 19 A 17 Note: Letters represent varieties (A, B, C, D) and numbers represent yields (i) Perform the analysis of variance to test at 0.05 significance level, the difference in the yields of varieties and in blocks. (ii) What would be the result if no blocking had been done, i.e., if we consider it as a completely randomized design? [20]
(20)

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About this paper

The 2024 CSS Statistics paper set by the Federal Public Service Commission. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet. Open the official paper beside the questions to check any of them.

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