Question

A. A small population of N = 12 has values of 2, 2, 3, 4, 4, 7, 8, 8, 8, 9, 12, 12. Take five samples of size 3 and calculate the mean for each. Then calculate the mean of these ten sample means. Is the mean of these sample means a good approximation of the population mean? Why or why not.

B. What is the concept being explored in A? In your own words, describe what this thereom says.

Answer 1

Population = (2, 2, 3, 4, 4, 7, 8, 8, 8, 9, 12, 12)

Samples with random numbers from above population are given as below:

S1 = (2,3,12), mean = 5.67

S2 = (2,7,8), mean = 5.67

S3 =(3,8,12), mean = 7.67

S4 = (3,4,9), mean = 5.33

S5 = (4,7,8), mean = 6.33

Mean of means = 6.133333

Population mean = sum of all observations / number of observations

Sum of all observations = 79

Number of observations = 12

Population mean = 79/12 = 6.58

Mean of sample means is seem to be closer to population mean.

Mean of sample means = 6.133333

Population mean = 6.58

The theorem says that unbiased estimator for population mean is approximately equal to the mean of sample means.