BSc Statistics SEM III 2022 2023 Oct 2023 STATISTICS II Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Answer the following questions
   • a) Correct the following if necessary: (10M)
   • i. If E(Parameter) = Statistic, then statistic is said to be an unbiased estimator
   • ii. Cost function is considered in Neyman’s allocation ili. is more efficient than SRSWOR
   • iv. Ratio estimator is always more efficient than estimate of population mean
   • v. Systematic sampling is not probability sampling
   • b) Answer in One sentence: (10M)
   • i. State any two limitations of stratified random sampling
   • ii. Define simple random sampling with replacement
   • iii. Write C.I. for population mean based on the sample of size n selected by
   • iv. Define ratio estimate of population mean. State its variance
   • v. State advantages of using cluster sampling
2. Q2 Attempt any TWO (20M)
   • a) Explain Probability of drawing a sample using Simple Random Sampling with Replacement and without replacement
   • b) Write characteristics of a good questionnaire
   • c) A simple Random Sample of size 3 is drawn from a population of size N with replacement. Let P; , and P3 be the probabilities of the sample containing 1, 2 and 3 different units respectively. Then show that P, = = j
3. Q3 Attempt any TWO (20M)
   • a) Describe the stratified random sampling procedure. How it is different from VCD/ SYB.Sc MARKS 3HRS
   • b) A population of size 2000 is divided into 4 strata. Their sizes and standard deviations are given below: A Stratified random sample of size 240 is to be drawn from the population Determine the sample sizes from these 4 stratum under: (i) Proportional allocation Explain why we need Stratification?
4. Q4 Attempt any TWO (20M)
   • a) Prove that for large sample V(r) = = (1- where = — RX;)?
   • b) A mathematics achievement test was given to 486 students prior to entering a certain college who then took a calculus class. A simple random sample of 10 students is selected and their calculus scures are recorded. It is known that average achievement test score for the 486 students was Estimate the average score by using regression estimation and estimate its S.E
   • c) i. State the disadvantages of systematic sampling
   • ii. Write a short note on cluster sampling
5. Q5 Attempt any TWO (20M)
   • a) i. In SRSWOR, the sample mean is an unbiased estimator of the population mean
   • ii. Compare SRSWR with SRSWOR
   • b) is minimum for fixed sample size
   • c) i. Distinguish between and regression estimation
   • ii. Explain the procedure of two stage sampling

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