Statistics

100 marks · 3 hours · 5 questions · official PDF, 3 pages

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Statistics · all years Q. 2 · (a) Define Type I and…Q. 3 · (a) Explain the concept of…Q. 4 · Explain the difference between Parametric…Q. 5 · Define conditional probability with examples.Q. 7 · Suppose you want a confidence…With this paperPart-I MCQs18 Official PDF3 pp ← 2025

3 hours · questions hide until you reveal them

Section A

Q. 2

(a) Define Type I and Type II errors in hypothesis testing. Explain the trade-off between these errors.

(b) The first four moments of a frequency distribution about the origin are $\mu_1' = -0.55, \quad \mu_2' = 4.46, \quad \mu_3' = -0.43$ and $\mu_4' = 68.52$ . Find skewness and kurtosis. Also comment on the shape of the data distribution.

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Q. 3

(a) Explain the concept of exchangeability in probability. How does it differ from independence?

(b) Define skewness of a distribution. What are the different measures of skewness?

(i) In a frequency distribution, the coefficient of skewness based upon quartiles is 0.6. If the sum of the upper and lower quartiles is 100 and median is 38, find the values of $Q_1$ and $Q_3$ .

(ii) Karl Pearson’s coefficient of skewness of a distribution is 0.32. If the standard deviation is 6.5 and mean is 29.6, determine the mode and the median of the distribution.

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Q. 4

(a)Explain the difference between Parametric and Non-Parametric tests. Provide examples of each in the context of ANOVA. [10]
(b)A secretary makes 2 errors per page, on average. What is the probability that on the next page he or she will make 4 or more errors? No error? [10]

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Q. 5

(a)Define conditional probability with examples. [10]
(b)In a small town only three newspapers, A, B, and C, are available for the readers. Suppose that 60% of readers subscribe to newspaper A, 40% subscribe to newspaper B, and 30% to newspaper C. Suppose also that 20% of them subscribe to both A and B, 10% subscribe to both A and C, 20% subscribe to both B and C, and 5% subscribe to all three newspapers. Construct Venn Diagram to present the above situation. What percentage of newspaper readers subscribe at least one of the three newspapers? What percentage of newspaper readers subscribe none of the three newspapers? [10]

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Section B

Q. 7

(a)Suppose you want a confidence interval for a Normal Mean with small sample size. Explain how would you construct it. [10]
(b)The population and death of two towns, according to age groups are given below: Age group Town A Town B Population No. of deaths Population No. of deaths Under 10 100 40 1000 300 11---25 1500 150 500 40 26---50 850 108 400 24 Above 50 50 37 100 6 Calculate crude death rate for town A Calculate SDR of town A taking the population of town B as a standard population. [10]

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About this paper

The 2026 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.

Disclaimer Prep Right is independent and not affiliated with FPSC.

Section A

Section B

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