A target population consists of 1000 companies. A researcher wants to estimate t

Question

A target population consists of 1000 companies. A researcher wants to estimate the percentage of companies exporting their products to other countries. Therefore, he selects a simple random sample of 50 companies without replacement.

a. Compute the variance of the sample percentage of exporting companies, assuming that 360 out of 1000 companies indeed do so.

b. Estimate the variance of the sample percentage, assuming the population percentage is unknown and there are 18 exporting companies in the sample.

c. Estimate the variance of the sample percentage, assuming the population percentage is unknown and there are 14 exporting companies in the sample.

d. Estimate the variance of the sample percentage, assuming the population percentage is unknown and there are 22 exporting companies in the sample.

Explanation / Answer

Solution:-

a) The variance of the sample percentage of exporting companies, assuming that 360 out of 1000 companies indeed do so is

n = 1000

x = 360

p = 0.36

Sample percentage of exporting companies = 36%

Variance = n × p × (1 - p)

Variance = 1000 × 0.36 × 0.64

Variance = 230.4

b) The variance of the sample percentage, assuming the population percentage is unknown and there are 18 exporting companies in the sample.

n = 50

x = 18

p = 18/50 = 0.36

Variance = n × p × (1 - p)

Variance = 50 × 0.36 × 0.64

Variance = 11.52

c) The variance of the sample percentage, assuming the population percentage is unknown and there are 14 exporting companies in the sample is 10.08

n = 50

x = 14

p = 14/50 = 0.28

Variance = n × p × (1 - p)

Variance = 50 × 0.28 × 0.72

Variance = 10.08

d) The variance of the sample percentage, assuming the population percentage is unknown and there are 22 exporting companies in the sample is 12.32

n = 50

x = 22

p = 22/50 = 0.44

Variance = n × p × (1 - p)

Variance = 50 × 0.44 × 0.56

Variance = 12.32

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