## Saturday, April 21, 2018

2017
(May)
STATISTICS
(General)
Course: 401
(Sample Survey)
Full marks: 48
Pass Marks: 14
Time: 2 hours
The figures in the margin indicate full marks for the questions

1. Find out the correct answer: 1x4=4
1. Sampling is inevitable in the situation(s)
1. Blood test of a person.
2. When the population is infinite.
3. Testing of life of dry battery cells.
4. All of the above.
1. Which one of the following sampling techniques does not involve probability in the selection of the sample?
1. Purposive sampling.
2. Simple random sampling.
3. Stratified sampling.
4. None of the above.
1. In case of stratifies sampling which of the following statements is true?
1. Lesser the number of strata, better it is.
2. More the number of strata, poorer it is.
3. More the number of strata, better it is.
4. None of the above.
1. Under equal allocation in stratified sampling the sample size from each stratum is
1. Proportional to stratum size.
2. Of same size from each stratum.
3. In proportion to the per unit cost of survey of the stratum.
4. All of the above.
2. Answer the following questions: 3x4=12
1. Distinguish between judgement sampling and probability sampling.
2. Give the concept of sample survey with suitable real life examples.
3. What is meant by stratified random sampling?
4. Give a description of systematic sampling.
3. Answer any two of the following: 8x2=16
1. Explain clearly the following terms with suitable examples: 2+2+2+2=8
1. Population
2. Sample
3. Parameter
4. Statistic
1. What is simple random sampling (SRS) procedure? Discuss briefly the methods of selecting an SRS. Enumerate the merits and demerits of SRS procedure.
2. With usual notation, in simple random sampling prove that. In simple random sampling with replacement, show that. 8
4. Answer any two of the following: 8x2=16
1. How do you estimate the population mean from stratified random sampling? Mention advantages of stratified sampling over simple random sampling. 5+3=8
2. Show that
1. Under what circumstances systematic sampling technique is employed? Mention the advantages and disadvantages of this method. From a population of 400 items, how will you select a sample of size 20 employing this technique? Explain.
(Old Course)
(Design of Experiment and Sample Survey)
Full marks: 80
Pass Marks: 32
Time: 3 hours
1. Write True or False: 1x8=8
1. With the help of analysis of variance, null hypothesis cannot be tested.
2. Randomized Block Design (RBD) is based on all the three basic principles (replication, randomization and local control) of design of experiment.
3. Analysis of variance cannot be applied in developing countries like India.
4. In the field layout of randomized block design (RBD) the blocks are formal in the direction parallel to fertility gradient.
5. Sampling is inevitable in the case of blood test of a person.
6. In simple random sample, probability is not applied.
7. In case of stratifies sampling more the number of strata better it is.
8. For drawing sample from infinite population systematic sampling technique is the best.
2. Answer the following questions: 3x9=27
1. What is meant by analysis of variance?
2. What is liner model? Write briefly about different types of linear model.
3. Write down the basic principles of a good experimental design.
4. Give the skeleton of analysis of variance (ANOVA) table of Latin square design.
5. What is factorial experiment?
6. Distinguish between judgement sampling and probability sampling.
7. Write down the usefulness of sample survey.
8. What is meant by stratified random sampling?
9. Under what circumstances systematic sampling technique is the best?
3. (a) What are the basic assumptions associated with analysis of variance? Write down the uses of analysis of variance technique. 7
Or
(b) Give an outline of the analysis of variance of two-way classified data. 7
4.  (a) Explain the basic principles of design of experiment. 7
Or
(b) Under what situation will you prefer RBD over CRD? Explain the methods of randomization in CRD and RBD. Write down the mathematical model in an RBD. 7
5. (a) What is Latin square design? Briefly discuss the analysis of variance of indicating the important steps. 7
Or
(b) Give the layout of a 4 x 4 Latin square design. Discuss briefly the advantages and disadvantages of an LSD. 7
6. (a) Explain clearly the following terms with suitable examples. 6
1. Population
2. Sample.
3. Parameter.
Or
(b) Discuss the advantages of sample survey over complete enumeration. 6
7. (a) Prove that in stratifies sampling the sample mean is an unbiased estimate of the population mean. 6
Or
(b) Show that in usual notation is stratifies sampling the variance of sample mean is given by
6
8. Write short notes on: 3x4=12

1. Pilot survey.
2. Statistic.
3. Simple random sampling without replacement.
4. Systematic sampling.