Question

A. A small population of N = 12 has values of 2, 2, 3, 4, 4,...

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.

Homework Answers

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.

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