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## Statistics

problem 1:

a) Illustrate sampling and non-sampling errors. What are random number tables? Describe their use.
b) describe the functions of CSO.

problem 2:

a) Describe the fundamental principles of a sample survey.
b) describe the functions of NSSO.

problem 3:

a) Define SRS:

• With replacement
• Without replacement from a finite population.

Derive the unbiased estimates of the population mean and its variance based on the above methods. Compare the efficiencies of the estimates of the population mean.

b) Describe stratified sampling. Describe how the gain due to stratification is accomplished.

problem 4:

a) Find out the size of the simple random sample for specified precision. What are the different methods of allocating a sample in stratified sampling?

b) In srswor obtain the variance of the estimate of the population proportion.

problem 5:

a) Describe systematic sampling. Obtain the variance of the estimated mean.

b) What do you mean by cluster sampling? Find out the optimum cluster size for fixed cost.

problem 6:

a) Describe the concept of circular systematic sampling. Obtain the variance of the estimated mean in clusters of equivalent sizes.

b) If the population comprises of linear trend then prove that stratified random sampling is more efficient as compared to systematic and simple random sampling.

problem 7:

a) Describe pps sampling with replacement. Obtain the variance of an unbiased estimate of the population total.

b) Describe two phase sampling. In two-phase sampling with equal number of second phase units obtain the variance of an unbiased estimate of the population mean.

problem 8:

a) Describe the concept of multi-stage sampling. Give any two applications of two-stage sampling.

b) Describe a method of choosing a pps sample with replacement. Obtain the variance of the estimated mean.

problem 9:

a) Show that the ratio estimator is the best linear unbiased estimator under the conditions to be stated by you.

b) Describe the regression estimates in stratified sampling and assess their efficiencies.

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M94988

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