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PPSC · PMS Punjab 2016

Statistics

100 marks · 3 hours · 7 questions
This paper Statistics · all yearsQ. 1 · Write short note on the…Q. 2 · Describe the general procedure for…Q. 3 · A Laboratory technician wants to…Q. 4 · Define an Index number. Discuss…Q. 5 · A sample of 9 parts…Q. 6 · What are the various statistical…Q. 7 · What are vital statistics? Describe…With this paper2019 →
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Q. 1

Write short note on the following:-

  1. (a)Probability and Non-Probability Sampling. [4]
  2. (b)Simple Random Sampling and Stratified Random Sampling. [4]
  3. (c)Properties of a good estimator. [4]
  4. (d)Type I and Type II error. [4]
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Q. 2
  1. (a)Describe the general procedure for testing a hypothesis about a population parameter.
  2. (b)According to a survey, the starting salary for an entry-level position in investment banking was 47 , 120 i n 2015.
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(10)
Q. 3
  1. (a)A Laboratory technician wants to compare the breaking strength of three kinds of thread. Originally he had planned to repeat each determination six times. Not having enough time, however, he has to base his analysis on the following results (in ounces): Col 1 Col 2 Col 3 Col 4 Col 5 Col 6 Thread 1 18.0 16.4 15.7 19.6 16.5 18.2 Thread 2 21.1 17.8 18.6 20.8 17.9 19.0 Thread 3 16.5 17.8 16.1 —— Perform an analysis of variance to test at 0.05 level of significance whether the differences among the sample means are significant. [10]
  2. (b)What is meant by an experimental design? Describe in brief the basic principles of experimental designs. [10]
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(20)
Q. 4
  1. (a)Define an Index number. Discuss the main steps involved in the construction of wholesale price index number. [5]
  2. (b)The following table gives average annual prices of ten commodities during the years 1990 and 1994. Calculate the consumer price index number for 1994 on the basis of 1990. Commodity Quantity consumed Unit of Price Price in 1990 (Rs 00) Price in 1994 (Rs 00) Wheat 20 kgs Rs. per kg 1.25 1.50 Rice 10 kgs Rs. per kg 3.00 3.75 Pulse 12 kgs Rs. per kg 2.50 3.00 Sugar 4 kgs Rs. per kg 2.00 3.25 Ghee 3 kgs Rs. per kg 3.75 4.00 Milk 30 litres Rs. per litre 0.50 0.75 Vegetables 35 kgs Rs. per kg 0.25 0.40 Fuel 200 kgs Rs. per kg 0.50 0.75 Cloth 22 meters Rs. per meter 1.50 2.10 House Rent 1 unit Rs. per unit 30.00 60.00 [8]
  3. (c)What is meant by seasonal variation? Explain how seasonal variations are measured and removed from the time series data? [5]
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Q. 5
  1. (a)A sample of 9 parts produced by certain production process are measured as 5, 7, 2, 4, 8, 9, 8, 6 and 5 inches respectively. Test the hypothesis that the process has the variance equal to 4 (inches)² at the 5% level of significance. [5]
  2. (b)Explain Non-parametric statistics. In what situations non-parametric procedures should be used? [6]
  3. (c)Given the two samples below, test the null hypothesis that the population medians are equal against the alternative that M₁ Sample1. 26, 25, 38, 33, 42, 40, 44, 26, 25, 43, 35, 48, 37 Sample 2 44, 30, 34, 47, 35, 46, 35, 47, 48, 34, 32, 42, 43, 49, 46, 47 [9]
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Q. 6
  1. (a)What are the various statistical organizations in Pakistan? Discuss the main sources of statistical data in Pakistan. [10]
  2. (b)The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution X 4 5 6 7 P(X=x) 0.2 0.4 0.3 0.1 Find the mean µ and standard deviation of X Find the mean μₓ and variance σ²ₓ of the mean X for random samples of 36 cherry puffs. [10]
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(20)
Q. 7
  1. (a)What are vital statistics? Describe the system for collection of vital statistics in Pakistan. Discuss its strong and weak points and suggest remedies. [8]
  2. (b)The employees in 4 different firms are distributed in three cell frequencies shown in the following table. Test the hypothesis that there is no relation between the firm and the type of labour. Let the level of significance be 5% Firm A B C D Type of labour Skilled 29 24 23 49 Semi-skilled 32 60 37 51 Mannual 24 56 40 80 [10]
  3. (c)Define power of a test. [2]
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(20)

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The 2016 PMS Punjab Statistics paper set by the PPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.

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