ANU UG B.Sc 5th Sem Sampling Techniques and Design of Experiments Important Questions

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UNIT-I (Sampling Theory)

10 Marks Questions:

1. Explain the principle steps in a sample survey.[ANU-17,19]
2. What are sampling and non-sampling errors? Describe the sources of  non-sampling errors.
3. What are sampling and non-sampling errors? Distinguish between probability and non-probability sampling methods.[ANU-17]
   
4. What are the types of sampling techniques and explain.[ANU-19]
5. What are the main steps involved in a sample theory. Discuss them briefly.
6. Explain the sources of errors in a sample survey and describe how there can be controlled.[ANU-18]
7.  Explain sampling and describe censuses versus sampling survey. Also write advantages and disadvantages of sampling over census.[ANU-18]
8. write the procedure of draw random samples from binomial population by using random numbers.
   

5 Marks question

1. In what respects sample survey is superior to a census survey? (OR)
2. What are the advantages of sampling over census.[ANU-17,18,19]
   
3. Explain purpossive sampling. What are its merits and demerits?[ANU-17]
4. Define population and types of population.
5. What are the requirements of a good sample.
6. Explain the methods of drawing a simple random sample.[ANU-17,18]
7. What are the reason for sampling biases.
8. Define random sampling. why is it preferred to other methods of selection of sample.
9. What are the advantages and limitations of sampling?
10. Explain the term i) sample unit ii) Statistics iii) Parameters iv) population v) sampling distribution
    
11. Explain the method of estimating stratified random sampling.
12. Explain the concept of complete census.
13. Explain the role of sampling frame in conducting  a sample survey. 
14. Explain the sources of errors in a sample survey.[ANU-19] 
15. Explain the method of simple random sampling. Show that sample mean is an unbiased estimator of population mean.

UNIT-II (Simple Random Sampling)

 10 Marks questions

1. With usual notation, show that V(yn)=(1-f)s2/n in SRSWOR.
2. In SRSWOR show that E(S2)=σ2.
3. In SRSWOR show that E(S2)=S2.
   
4. Describe the methods of selection of a simple random sample.[ANU-18]
5. Prove that V(yn)=N-n/N.S2/n
6. In simple random sampling without replacement, Show that the variance of  sample mean is given by V(yn)=N-n/N.S2/n [ANU-19]
7. In simple random sampling without replacement, derive its standard error.[ANU-19]
   
8. Explain the SRSWOR and SRSWR and also discuss the selection procedure for  obtaining a simple random sample by lottery method.
9. Explain random number techniques for obtaining a SRS.
10. In SRSWOR, Show that sample mean is an unbiased estimate of population mean. Derive its standard error.
11. In SRSWOR, Show that sample mean square is an unbiased estimate of population mean.
    
12. Explain the method of SRS. Also obtain variance of sampling in case of SRSWOR.[ANU-18]
13. Explain simple random sampling. Describe the methods of drawing an SRS. 
14. In SRSWOR, the variance of the sample mean is given by Var(yn)=Sv/n(N-n/N)
15. Derive an expression to find the variance of sample means in SRSWR. Also compare the variance in SRSWOR and SRSWR.
16. Define simple random sampling. Explain the merits and demerits of a simple random sampling.
17. Obtain an unbiased estimation of population mean SRSWOR.[ANU-17]
18. In SRSWOR obtain the variance of the sample means.[ANU-17]
    

5 Marks Questions

1. In SRSWR obtain variance of sample mean.
2. Sate advantages and disadvantages of simple random sampling.
3. Distinguish between SRSWOR and SRSWR.[ANU-18]
4. Show that E(yst)=YN
5. Obtain the expression for Var(Yst).
6. Find the variance of the mean of SRS from a finite population.
   
7.  what are the Random number tables and their uses.
8. In SRSWOR, Show that sample mean square coefficient is an unbiased estimate of population mean. 
9. Explain simple random sampling (a) With Replacement b) without replacement with suitable examples.
   

UNIT-III ( Stratified random sampling and Systematic sampling)

 10 Marks Questions

1. Explain stratified random sampling with proportional and optimum allocation. Obtain the variances of the estimated mean in proportional and optimum allocation.
2. In the usual notation prove that V(yst)<=V(Ysys)r<=V(Yn)R [ANU-17,19]
3. Show that V(Yst)Ney<=V(Yst)Prop<=V(Yn)Ran
   
4. Explain stratified random sampling. Give it's advantages and disadvantages.
5. In Neyman's optimum allocation, show that ni ∝NiSi [ANU-19]
   
6. In the usual notation show that V(Yst)p>=V(Yst)N [ANU-17]
7. Define stratified random sampling, explain the need of stratification.
8.  what is stratified random sampling? Discuss and proportional allocation in stratified random sampling.
   
9. Obtain the variance of the estimated mean in stratified random sampling with proportional and optimum allocations.
10. Compare the variance in simple, stratified and systematic random sampling methods.
    

5 Marks Questions

1. Explain stratified random sampling.  Give any four of its applications.
   
2. Define systematic sampling. What are its advantages, disadvantages and applications?[ANU-17]
3. Derive the variance of stratified random sampling.
4. Explain the concept of systematic sampling.
5. Explain stratified random sampling. What are it's merits and demerits?[ANU-17]
6. Explain proportional  allocation.
7. Explain the need for stratification.[ANU-19]
8. what are the advantages of stratified sampling over simple random sampling?
   
9. How do you estimate population mean in proportional allocation?[ANU-18]
10. Explain Cochran's theorem.[ANU-18]
    

UNIT-III (Analysis of Variance)

10 Marks Questions

1. Define ANOVA  one way classification. write the statistical analysis of ANOVA one way classification.
2. Explain principles of design of experiments.
3. Explain the statistical analysis of two way classification.[ANU-18]
4. Explain the statistical analysis of one way classification.[ANU-19]
5. Explain the method of estimating of parameter in ANOVA two way classification.
6. Explain the method of estimating of parameter in ANOVA one way classification.
7. Explain the ANOVA one-way classification
8. Explain the statistical analysis of one-way analysis of variance with unequal classification.[ANU-18].
9. Explain the statistical analysis of one-way analysis of variance with equal classification
   
10. what is the differences between " Variability within classes" and " Variability between classes"? Explain with suitable examples.
    
11. Explain the advantages and disadvantages of ANOVA. [ANU-19]
12. Explain in brief about the ANOVA for two-way classification data with  single observation per cell.
13. Explain the mathematical model of one-way ANOVA. Obtain the expectations of various sums of squares.[ANU-17]
14. Explain the mathematical model of two-way ANOVA. Obtain the expectations of various sums of squares.[ANU-17]

5 Marks Questions

1. Define ANOVA with assumptions.
   
2. Explain the necessity of ANOVA.
3. Define ANOVA. Bring out the main differences between analysis for one-way and two-way classification data.[ANU-18]
   

UNIT-V (design of experiments)

10 Marks Questions

1. Explain the statistical analysis of R.B.D with one missing observation.[ANU-17]
2. Explain the statistical analysis of L.S.D . Obtain the relative efficiency of LSD over CRD.
3. Derive the efficiency of a LSD as compared to a CRD.
4. Explain L.S.D. Explain its analysis.[ANU-17]
   
5. Explain the principle of an experimental design.[ANU-18]
6. Discuss the efficiency of RBD and CRD and that of LSD over RBD and CRD.[ANU-19,18]
7. Explain the analysis of Randomized Block design.[ANU-19]
   
8. Explain missing plot technique in LSD.
9. Explain layout of RBD and its statistical analysis.
   

5 Marks Questions

1. Explain the principles of experimental designs.[ANU-17]
2. Explain the concept of factorial experiment and its advantages.[ANU-17]
3. Write advantages of C.R.D.