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Pune University - SY BSc (Sem - I) STATISTICS - II : Statistical Techn, April 2010

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Total No. of Questions : 4] P279 [Total No. of Pages : 3 [3717] - 122 S.Y. B.Sc. STATISTICS STT - 212 : Statistical Techniques - II (Semester - I) (Paper - II) (New Course) Time : 2 Hours] [Max. Marks : 40 Instructions to the candidates : 1) All questions are compulsory. 2) Figures to the right indicate full marks. 3) Use of calculator and statistical tables is allowed. 4) Symbols and abbreviations have their usual meaning. Q1) Attempt each of the following: a) Choose the correct alternative in each of the following: i) In sampling with proportions under SRSWOR, the standard error of estimator of population proportion is given by A) B) PQ n n PQ ( 1) n D) n 2 S n C) ii) [1 Each] S2 n In stratified random sampling with optimum allocation, the size of ith stratum sample is given by A) ni = n Wi Si B) ni = n Wi ni = n Wi Si2 D) ni = n C) Wi Si k Wi Si i =1 where Wi = i iii) In double sampling plan, the decision of accepting or rejecting a lot can not be taken based on first sample if number of defectives in the first sample (d1) is d1 c1 A) d1 > c2 B) C) D) c1 + 1 d1 c2 d1 > O P.T.O. b) State whether each of the following statements is true or false:[1 Each] i) The number of simple random samples of size 3 that can be drawn from a population consisting of 6 units by SRSWR is 63. ii) In, sampling with proportions under SRSWOR, the estimator of population proportion is sample proportion (p). iii) In single sampling plan, probability of acceptance of lot ( p a) increases with the increase in the value lot quality p. c) Define ATI for single sampling plan. [1] d) State the estimator of population total under SRSWR. [1] e) What is the role of acceptance number C in single sampling plan? [1] f) In stratified random sampling under proportional allocations determine n1 & n2 if N1 = 2500, N2 = 1500 and n = 200. [1] Q2) Attempt any two of the following: [5 Each] a) Explain the term sampling for proportion . Give one real life situation suitable for it. State estimator of population proportion and standard error of it under SRSWR. b) Given the following information, obtain the estimate of population mean under stratification and the estimate of standard error of this estimator. Stratum (i) ni xn si (sample s.d.) 1 500 40 15 5 2 300 35 12 6 3 c) Ni 200 25 10 5 Explain the terms: i) AQL. ii) Q3) Attempt any two of the following: a) i LTPD. [5 Each] Explain stratified random sampling method. Give a real life situation where this method is applicable. [3717] - 122 2 b) In SRSWOR, prove that probability of a specified unit being selected in a sample at any given draw is equal to the probability that it is selected at the first draw. c) For a double sampling plan, { N = 1000, n1 = 50, n2 = 100, c1 = 0, c2 = 1} find the probability of rejecting the lot of quality p = 0.01. Q4) Attempt any one of the following: a) Explain the working of a double sampling plan. State the expression for AOQ for the double sampling plan. [6] ii) Write down all possible samples of size 2 from population {1, 1, 2, 4, 6} by SRSWOR and verify whether sample mean is unbiased estimator of population mean. [4] i) Draw an OC - curve for the single sampling plan {N = 1000, n = 50, c = 0} taking lot quality p = 0.01, 0.05, 0.1, 0.2 and 0.5.[6] ii) b) i) Explain the terms: 1) Producer s risk. 2) Consumer s risk. [4] Y [3717] - 122 3

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Additional Info : S.Y. B.Sc. Statistics (Semister - I), STT - 212 : Statistical Techniques - II (Paper - II) (New Course), Pune University
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