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.
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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