A population consists of the following four values 81012and

A population consists of the following four values: 8,10,12,and 16. From this population, there are 6 different samples of size 2. The means of the 6 samples of size 2.  The means of the 6 samples of size 2 are 9,10,12,11,13,and 14. Compute thhe mean of the distribution of the sample means and the population mean. Compare the two values. What is true about the two values?

Solution

population of four values: 8,10,12,and 16

Mean of the values of the population = (8 + 10 + 12 + 16)/4 = 11.5

Mean of the distribution of sample means = (9 + 10 + 12 + 11 + 13 +14)/6 = 69/6 = 11.5

Both the values are equal

Hence the best estimate or point estimate of the population mean is the sample mean