The following table presents the rice production in 1985 in 43 countries. These

Question

The following table presents the rice production in 1985 in 43 countries. These figures for 65 of 191 countries in the world appear in the Statistical Abstract of the United States, 1990. The population of N = 43 productions is divided into two strata of sizes N_1 = 32 and n_2 = 11. The total, mean, variance, and standard deviation for the population of the N = 43 production in Table 1 are y = 157.27, y = 3.66, S^2 = 31.6 and s = 5.63. a. Consider a sample of size N = 10 from the n = 43 countries in the above table. Determine the sample sizes for strata 1 and 2 using the proportional allocation method. b. Calculate the variance, standard error and coefficient of variation of the sample means for each of the strata. c. Suppose a simple random sampling method leads to the selection of the samples of countries (4, 6, 9, 12, 17, 22, 31) and (1, 6, 10) from strata 1 and 2 respectively. i. Estimate the sample means and totals of the rice production in the two strata. ii. Find the variance and standard error of the estimates in (I). iii. Estimate the differences of the means and totals of the rice production in the two strata. iv. Find the standard error of the estimates in (iii). v. Find the 95% confidence limits for the differences.

Explanation / Answer

a) The sample size from the two strata is 10.

n(first strata) = 32

n(second strata) =11

In propportion allocation method, the sample size from each of the strata on the total sample will be based on the proportions of the two strata.

Applying the same

Proportion of 1st strata = 32/43 = 74.4 %

Proportion of 2nd strata = 11/43 = 25.6 %

Applying similar proportions for a sample of size 10, 7.4 observations will come from strata 1 and 2.6 observation will come from starta 2.

Rounding off the same,

Sample size from strata 1 = 7

Sample size from strata 2 = 3

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