IGNOU MST 20 SOLVED ASSIGNMENT

Ques 1.

State whether the following statements are true or false and also give the reason in support of your answer:

a) If X and Y are uncorrelated, the V(Rag) reduces to that of Variance of Ratio Estimator of Population mean

b) Among all the members of the General Class of the estimators only Regression estimator is an unbiased estimator of the Population mean.

c) An Incomplete Block Design with the following parameters b=8,k=3,9=8,r=3 is found to be a Balanced Incomplete Block Design.

d) A One-half fractional factorial design of a 2ª full factorial design will be denoted by a 22 Factorial design.

e) The Cluster estimator ỹ, becomes an unbiased estimator of population mean only if M and , are uncorrelated

Ques 2.

Suppose we wish to estimate the total number of Cows in 2026 in certain state. The total number of cows for 2024 was X = 5000. The Sampling unit was the farm, and it is assumed that there has been no change in the number of farms which we shall assume to be N=500. A sample of n=20 farms is selected, and the data is as follows:

Estimate the average number of cows for 2026 by Ratio Method of estimation and obtain the estimate of the MSE of Ratio estimator of Population Mean

Ques 3.

Define the difference estimator for the population mean. Show that it is an unbiased estimator and its variance is given by where symbols have their usual meanings. 

Ques 4.

A population consisting of 6 clusters, each of size 6 is given below. The values of the study variable Y, noted on each of the units within each cluster are also provided. A random sample of size 3 clusters was selected from the population and 3 elementary units from the selected clusters were randomly chosen

Let the 2 nd, 4th and 6thclusters be selected randomly in the first-stage sample. Further, let the y-values 2, 7, 3 of the 2nd cluster; 6, 3, 1 of the 4th cluster and 7, 4, 3 of the 6th cluster be selected randomly for the second-stage sample

Estimate the population mean on the basis of the suggested estimator and compare it with the actual value of the population mean

Ques 5.

Suggest an estimator of population mean in cluster sampling with unequal size clusters, which is based upon the means of selected clusters. Determine whether it is an unbiased estimator?

Ques 6.

Below is given the plan and yields of 2² -Factorial Experiment involving 2 factors A and B each at two levels 0 and 1. Analyse the design

Does treatment effect A differs from treatment effect B?

Ques 7.

Explain what is meant by a one-quarter fractional factorial experiment of a 2 ² factorial experiment. Give a notation which denotes the one-quarter fractional factorial design.

Ques 8.

Let us consider the following Balanced Incomplete Block Design (B.I.B.D.) with parameters

Obtain a derived design from the above Balanced Incomplete Block Design (B.I.B.D.) and find the parameters of the obtained design.

Ques 9.

Define the Residual B.I.B.D. and Derived B.I.B.D. of a given symmetric B.I.B.D. Mention the rule of constructing a residual B.I.B.D. corresponding to a specific B.I.B.D.

then (X, ) is a (5, 3, 3)- B.I.B.D. Find the incidence matrix of this B.I.B.D.

Ques 10.

State whether the following statements are true or false and also give the reason in support of your answer:

a) If X and Y are uncorrelated, the V(Rag) reduces to that of Variance of Ratio Estimator of Population mean

b) Among all the members of the General Class of the estimators only Regression estimator is an unbiased estimator of the Population mean.

c) An Incomplete Block Design with the following parameters b=8,k=3,9=8,r=3 is found to be a Balanced Incomplete Block Design.

d) A One-half fractional factorial design of a 2ª full factorial design will be denoted by a 22 Factorial design.

e) The Cluster estimator ỹ, becomes an unbiased estimator of population mean only if M and , are uncorrelated

Ques 11.

Suppose we wish to estimate the total number of Cows in 2026 in certain state. The total number of cows for 2024 was X = 5000. The Sampling unit was the farm, and it is assumed that there has been no change in the number of farms which we shall assume to be N=500. A sample of n=20 farms is selected, and the data is as follows:

Estimate the average number of cows for 2026 by Ratio Method of estimation and obtain the estimate of the MSE of Ratio estimator of Population Mean

Ques 12.

Define the difference estimator for the population mean. Show that it is an unbiased estimator and its variance is given by where symbols have their usual meanings. 

Ques 13.

A population consisting of 6 clusters, each of size 6 is given below. The values of the study variable Y, noted on each of the units within each cluster are also provided. A random sample of size 3 clusters was selected from the population and 3 elementary units from the selected clusters were randomly chosen

Let the 2 nd, 4th and 6thclusters be selected randomly in the first-stage sample. Further, let the y-values 2, 7, 3 of the 2nd cluster; 6, 3, 1 of the 4th cluster and 7, 4, 3 of the 6th cluster be selected randomly for the second-stage sample

Estimate the population mean on the basis of the suggested estimator and compare it with the actual value of the population mean

Ques 14.

Suggest an estimator of population mean in cluster sampling with unequal size clusters, which is based upon the means of selected clusters. Determine whether it is an unbiased estimator?

Ques 15.

Below is given the plan and yields of 2² -Factorial Experiment involving 2 factors A and B each at two levels 0 and 1. Analyse the design

Does treatment effect A differs from treatment effect B?

Ques 16.

Explain what is meant by a one-quarter fractional factorial experiment of a 2 ² factorial experiment. Give a notation which denotes the one-quarter fractional factorial design.

Ques 17.

Let us consider the following Balanced Incomplete Block Design (B.I.B.D.) with parameters

Obtain a derived design from the above Balanced Incomplete Block Design (B.I.B.D.) and find the parameters of the obtained design.

Ques 18.

Define the Residual B.I.B.D. and Derived B.I.B.D. of a given symmetric B.I.B.D. Mention the rule of constructing a residual B.I.B.D. corresponding to a specific B.I.B.D.

then (X, ) is a (5, 3, 3)- B.I.B.D. Find the incidence matrix of this B.I.B.D.

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