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FPSC · CSS 2023

Statistics

100 marks · 3 hours · 7 questions · official PDF, 2 pages
This paper Statistics · all yearsQ. 2 · Calculate the Q1, median and…Q. 3 · From the following data, determine…Q. 4 · Derive the Poisson distribution as…Q. 5 · Draw all possible random sample…Q. 6 · The two samples A and…Q. 7 · The following data represent the…Q. 8 · (a) Given the population 1,…With this paperOfficial PDF2 pp← 20222024 →
3 hours · questions hide until you reveal them

SECTION–A

Q. 2
  1. (a)Calculate the Q1, median and Q3 from the following distribution of weight of containers in Kg, and comment on the symmetry of distribution. Weight (Kg) 18-26 27-35 36-44 45-53 54-62 63-71 72-80 # of Containers 13 20 39 40 25 6 12 [10]
  2. (b)What is frequency distribution? Discuss briefly the steps involve in construction of frequency distribution. [5]
  3. (c)The first three moments of a distribution about the value 2 of the variable are 1, 16 and -40. Show that the mean is 3, the variance 15 and m3 is -86. Also show that the first three moments about x=0 are 3, 24 and 76. [5]
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Q. 3
  1. (a)From the following data, determine the linear regression equations of X₁ on X3 and of X2 on X3. X₁ 07 12 14 17 20 X₂ 04 07 08 09 12 X₃ 01 02 04 05 08 Find the deviations of observed values of X₁ from the regression, i.e., X₁.|3. Repeat the same of X2, i.e., obtain X2.|3. Determine the simple correlation co-efficient between the two sets of deviations X1.|3 and X2.|3. [10]
  2. (b)What is meant by: Regression Regresand Regressor Regressor co-efficient [5]
  3. (c)Describe the Properties of the correlation co-efficient? [5]
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Q. 4
  1. (a)Derive the Poisson distribution as the limiting form of the binomial distribution, stating clearly the assumptions you make. [8]
  2. (b)Enumerate all the possible (i) combinations and (ii) permutations of 3 letters chosen from the four letters A, B, C, and D. [6]
  3. (c)A box contains 4 bad and 6 good tubes. Two tubes are drawn together at random. One of them is tested and found to be good. What is the probability that other one is good? [6]
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Section B

Q. 5
  1. (a)Draw all possible random sample of size n₁=2 with replacement from a finite population consisting of 4, 6, 8. Similarly draw all possible random samples n2=2 with replacement from another finite population consisting of 1, 2, 3. Find the possible difference between the sample means of the two populations. Construct the sampling distributions of X₁ - X₂ and compute its mean and variance. Verify that µₓ₁₋ₓ₂ = µ₁ - µ₂ and σ²ₓ₁₋ₓ₂ = σ²/N₁ + σ²/N₂ [12]
  2. (b)Explain sampling and non-sampling errors. What method would you suggest to control each type of error? [8]
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Q. 6
  1. (a)The two samples A and B detailed below, were taken from normal populations of standard deviation 0.8. Test whether the difference of means is significant A 10.5, 11.6, 12.7, 12.9, 13.5, 13.6, 14.8 B 11.3, 12.4, 12.4, 13.9, 14.2, 14.7, 14.9, 15.6 [12]
  2. (b)Explain with examples the difference between: Null and Alternative hypothesis Simple and composite hypothesis Type I-error and Type II-error Critical and non-critical region. [8]
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Q. 7
  1. (a)The following data represent the result of 3 questions obtained by 3 students in three subjects: Students Subjects English Mathematics Statistics 1 13 23 22 18 20 23 15 16 20 2 21 20 20 16 14 15 24 24 22 3 18 17 19 15 13 21 12 16 18 Perform an analysis of variance upon these data and test the hypothesis that: The subjects are of equal difficulty. The students are of equal ability, and The students and subjects do not interact. [12]
  2. (b)Discuss why using multiple two-sample t-tests is not an appropriate alternative of analysis of variance? [8]
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Q. 8

(a) Given the population 1, 1, 1, 3, 4, 5, 6, 6, 6, and 7. Find

(i) The probability that a random sample of size 36 selected with replacement will yield sample mean between 3.26 and 4.74

(ii) The mean and standard deviation for the sampling distribution of means for a sample size of 4 selected at random without replacement. Between what values would you expect at least 34\frac{3}{4} of the sample mean to fall?

(b) Explain sampling and non-sampling errors. What methods would you suggest to control each type of error?

(c) Explain with examples the following properties of a point estimator:

(i) Unbiasedness, (ii) Consistency, and (iii) Efficiency.

Checked against official paper
(20)

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About this paper

The 2023 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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