The farms raising cattle in Laguna were divided into 3 strata based on their land areas as reported in the 2001 Census of Agriculture (CA). Below is the summary of statistics derived from the 2001 CA. You were asked to undertake a simple cost of production survey.

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The farms raising cattle in Laguna were divided into 3 strata based on their land
areas as reported in the 2001 Census of Agriculture (CA). Below is the summary
of statistics derived from the 2001 CA. You were asked to undertake a simple cost
of production survey.
No. of cattle Average
farms in
Population
Variance
Stratum
no. of
Cattle per
farm
25
Laguna
Large
100
250
Medium
500
12
80
Small
1400
12
2000
a. Suppose that the per interview cost of surveying large farms is Php 300, while
in the medium farms, Php 600 and in small farms, Php750 and given a field
operations budget of Php 360,000, design a probability sample survey that will
render minimum variance for estimating cattle-related characteristics of interest.
b. Compare your results with the variance of the sample mean derived from a
design using proportional allocation of the same sample size from (a).
Transcribed Image Text:The farms raising cattle in Laguna were divided into 3 strata based on their land areas as reported in the 2001 Census of Agriculture (CA). Below is the summary of statistics derived from the 2001 CA. You were asked to undertake a simple cost of production survey. No. of cattle Average farms in Population Variance Stratum no. of Cattle per farm 25 Laguna Large 100 250 Medium 500 12 80 Small 1400 12 2000 a. Suppose that the per interview cost of surveying large farms is Php 300, while in the medium farms, Php 600 and in small farms, Php750 and given a field operations budget of Php 360,000, design a probability sample survey that will render minimum variance for estimating cattle-related characteristics of interest. b. Compare your results with the variance of the sample mean derived from a design using proportional allocation of the same sample size from (a).
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