BSc Sem III 2023 2024 2024 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 Sample is a part of universe
   • ii. | Sample Mean is an unbiased estimate of population proportion iii, Simple random sampling is better than systematic random sampling
   • iv. Regression estimator of population mean is a biased estimator of Y
   • v. Systematic sampling require Interval for random sample
   • b) Answer in One sentence: (10M)
   • i. Give any two advantages of Sampling
   • ii. Define parameter with example
   • iii. State the formula of prop iv State the mean of regression estimator for population
   • v. Write any.two Applications of sampling
2. Q2 Attempt any TWO
   • a) Write Merits and Demerits of Sample Survey
   • b) In SRSWOR, the Sample mean square is unbiased estimator of the population mean
   • c) Prove that, in SRSWR the variance of sample mean is V(y) = x= Attempt any TWO (20M)
   • a) Derive formula for sample sizes for samples to be drawn from various strata under proportional allocation
   • b) A population of size 1500 is divided into 3 strata. Their sizes and standard deviations are given below: A Stratified random sample of size 200 is to be drawn from the population Determine the sample sizes from these 3 stratu under: (i) Proportional allocation
   • c) Derive formula for optimum allocation VCD\ SEM-III Theory of Sampling
3. Q4 Attempt any TWO (20M)
   • a) Obtain the estimator of population mean using linear regression method of estimation when is not specified. Obtain value of for which variance is minimum and also obtain the formula for ‘ b) Ina locality there are 50 lanes. In 2005 there were 6250 persons living. Recently sample of 5 lanes showed the number of residents changing as following: Person living in 2005: 100 150 160 140 Estimate the standard error of the number of persons residing in the locality using
   • i) The recent sample only li) The information about 2005 as well as recent sample
   • c) Explain the systematic sampling procedure i) draw the sample of size 15 from population of size 400, using sample as 25
4. Q5 Attempt any TWO (20M)
   • a) i. write difference between Parametric and sampling
   • ii. Difference between Population survey anc sample survey
   • b) Derive confidence interval for population total,
   • c) Compare between Stratified sampling and Systematic sampling

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