A random sample of 6 clusters of 4 households each is select

A random sample of 6 clusters of 4 households each is selected from a population of 50 such clusters by SRSWOR. The total amount of income tax paid for each household in the 6 clusters was as follows (data in thousands of dollars). Set up the sample ANOVA table. Estimate the relative efficiency of this cluster sample design compared to a simple random sample of 24 households. Estimate the numerical value of the intra-cluster correlation coefficient.

Solution

Source DF SS MS F P
C2 5 2272.33 454.47 54.90 0.000
Error 18 149.00 8.28
Total 23 2421.33

S = 2.877 R-Sq = 93.85% R-Sq(adj) = 92.14%

b) cluster variance 94.62

srs variance 100.625

hence cluster sampling is more efficient

c) 0.928388