State whether the following statements are true or false and also give the reason in support of your answer:
a) In Two-Stage Sampling if , it becomes the Cluster Sampling.
b) Among all the members of the General Class of the estimators only Product estimator is an unbiased estimator of the Population mean.
c) With the following parameters , an Incomplete Block Design is found to be a Balanced Incomplete Block Design.
d) a 23 Factorial design is One-half fractional factorial design of a 26 full factorial design.
e) If Mi and are correlated, the Cluster estimator
becomes an unbiased estimator of the Population Mean.
a) True. In two-stage sampling, if all the secondary units within each selected primary unit are observed (i.e., complete enumeration within selected clusters), the design reduces to cluster sampling because each selected primary unit is treated as a cluster and all its elements are included. b) False. The product estimator of the population mean is generally a biased estimator, though it may have smaller mean square error under certain conditions __________ ____ ______ _____ _______ ______ _________ _________ __________.
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In a population of size 500, the population mean of the auxiliary variable X was observed to be 834.00. On the basis of a sample of size 40, the following sample values were obtained:
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$y = 740.00; \bar{x} = 865.00; s_y^2 = 9560.00; s_x^2 = 15300.00; s_{yx} = 30540.2.$
Obtain the values of the regression estimate and the ratio estimate of the population mean as obtained on the basis of the sample drawn. $\quad \quad \quad \quad \quad \quad \quad \quad (08)$
Following data presents a population of 10 clusters of size 3 each. Each cluster represents a bunch of students of standard IV in a school. The marks obtained by students in a competitive test (out of 75 marks) have been shown in the data set. Find the Relative Efficiency (R.E.) of the Cluster Sampling with respect to the Simple Random Sampling without Replacement scheme:
In a population of size 500, the population mean of the auxiliary variable X was observed to be 950.00. On the basis of a sample of size 30, the following sample values were obtained:
Obtain the value of the Ratio estimate of population mean as obtained on the basis of the sample drawn. Also, find the estimated value of the Sample Mean Squared Error of the estimate.
State whether the following statements are true or false and also give the reason in support of your answer:
a) In Two-Stage Sampling if , it becomes the Cluster Sampling.
b) Among all the members of the General Class of the estimators only Product estimator is an unbiased estimator of the Population mean.
c) With the following parameters , an Incomplete Block Design is found to be a Balanced Incomplete Block Design.
d) a 23 Factorial design is One-half fractional factorial design of a 26 full factorial design.
e) If Mi and are correlated, the Cluster estimator
becomes an unbiased estimator of the Population Mean.