Question

Consider a random sample (WOR) of two industries from a population of 5
industries having yearly turnover as follows:

Industry Turnover (in lakhs)
1 2000
2 2400
3 1800
4 3000
5 2600

Enumerate all possible samples (WOR) of size two and show that the sample
mean gives an unbiased estimate of population mean

Answer 1

Question #65437, Math / Statistics and Probability

Consider a random sample (WOR) of two industries from a population of 5 industries having yearly turnover as follows:

Industry Turnover (in lakhs)

1 2000

2 2400

3 1800

4 3000

5 2600

Enumerate all possible samples (WOR) of size two and show that the sample mean gives an unbiased estimate of population mean

Answer.

$$\text{Population mean } \mu = \frac{1}{5} (2000 + 2400 + 1800 + 3000 + 2600) = 2360.$$ $$\text{Mean of sample means: } \mu_{\overline{x}} = \frac{1}{10} (2200 = 1900 + 2500 + 2300 + 2100 + 2700 + 2500 + 2400 + 2200 + 2800) = 2360.$$ $$\text{So } \mu_{\overline{x}} = \mu.$$

Answer provided by www.AssignmentExpert.com