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

- Sampling is inevitable in the situation(s)

- Blood test of a person.
- When the population is infinite.
- Testing of life of dry battery cells.
- All of the above.

- Which one of the following sampling techniques does not involve probability in the selection of the sample?

- Purposive sampling.
- Simple random sampling.
- Stratified sampling.
- None of the above.

- In case of stratifies sampling which of the following statements is true?

- Lesser the number of strata, better it is.
- More the number of strata, poorer it is.
- More the number of strata, better it is.
- None of the above.

- Under equal allocation in stratified sampling the sample size from each stratum is

- Proportional to stratum size.
- Of same size from each stratum.
- In proportion to the per unit cost of survey of the stratum.
- All of the above.

2. Answer the following questions: 3x4=12

- Distinguish between judgement sampling and probability sampling.
- Give the concept of sample survey with suitable real life examples.
- What is meant by stratified random sampling?
- Give a description of systematic sampling.

3. Answer any two of the following: 8x2=16

- Explain clearly the following terms with suitable examples: 2+2+2+2=8

- Population
- Sample
- Parameter
- Statistic

- What is simple random sampling (SRS) procedure? Discuss briefly the methods of selecting an SRS. Enumerate the merits and demerits of SRS procedure.
- 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

- How do you estimate the population mean from stratified random sampling? Mention advantages of stratified sampling over simple random sampling. 5+3=8
- Show that

- 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

- With the help of analysis of variance, null hypothesis cannot be tested.
- Randomized Block Design (RBD) is based on all the three basic principles (replication, randomization and local control) of design of experiment.
- Analysis of variance cannot be applied in developing countries like India.
- In the field layout of randomized block design (RBD) the blocks are formal in the direction parallel to fertility gradient.
- Sampling is inevitable in the case of blood test of a person.
- In simple random sample, probability is not applied.
- In case of stratifies sampling more the number of strata better it is.
- For drawing sample from infinite population systematic sampling technique is the best.

2. Answer the following questions: 3x9=27

- What is meant by analysis of variance?
- What is liner model? Write briefly about different types of linear model.
- Write down the basic principles of a good experimental design.
- Give the skeleton of analysis of variance (ANOVA) table of Latin square design.
- What is factorial experiment?
- Distinguish between judgement sampling and probability sampling.
- Write down the usefulness of sample survey.
- What is meant by stratified random sampling?
- 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

- Population
- Sample.
- 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

- Pilot survey.
- Statistic.
- Simple random sampling without replacement.
- Systematic sampling.