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FPSC · CSS 2022

Statistics

100 marks · 3 hours · 6 questions
This paper Statistics · all yearsQ. 2 · What can you say of…Q. 3 · ( 6 − 3 6…Q. 9 · Explain the six steps of…Q. 10 · Given the following ANOVA for…Q. 11 · Define the relative efficiency. How…Q. 13 · Describe the importance of vital…With this paper← 20212023 →
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SECTION–A

Q. 2

What can you say of the skewness in each of the following cases?

  1. (a)i) The median is 60 while the two quartiles are 40 and 80. ii) Mean = 140 and Mode = 140. [9]
  2. (b)The first three moments about 16 are respectively -0.35, 2.09 and -1.93.
  3. (c)Discuss the various measures or quantities by which the characteristics of frequency distributions are measured and compared. [6]
  4. (d)Differentiate between descriptive and inferential statistics. [5]
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(20)

Section B

Q. 3

( 6 − 3 6 − 1 ) = 4.824 ( 3 5 ) = 2.894 \text{Var}(\bar{X}) = \frac{14.472}{3} \left( \frac{6-3}{6-1} \right) = 4.824 \left( \frac{3}{5} \right) = 2.894 Var ( X ˉ ) = 3 14.472 ​ ( 6 − 1 6 − 3 ​ ) = 4.824 ( 5 3 ​ ) = 2.894 Discrepancy due to rounding; calculated variance matches theoretical derivation. 8 A candidate for mayor in a large city believes that he appeals more of the women voters than the men voters. He hires the services of a poll-taking organization, and they find that 62 out of 100 women interviewed support the candidate, and 69 out of 150 men support him. Calculate 99% confidence interval for the difference between two proportions.

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(10)
Q. 9

Explain the six steps of Tests of Hypothesis.

(10)
Q. 10

Given the following ANOVA for a RCB design

  1. (a)Complete the analysis; fill in the mean squares ANOVA Table Completion To complete the Analysis of Variance (ANOVA) table for a Randomized Complete Block (RCB) design, we utilize the relationship M S = MS=SSdfMS = \frac{SS}{df} .
  2. (b)Compute the standard error for a treatment and for the difference between two treatment means.
  3. (c)Treatment means are 1.464, 1.195, 1.325 and 1.662.
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(12)
Q. 11

Define the relative efficiency. How would you calculate the relative efficiency of LS design relative to RCB design with rows as blocks?

(8)
Q. 13

Describe the importance of vital statistics. Also state its uses and limitations.

(8)

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About this paper

The 2022 CSS Statistics paper set by the FPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.

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