The following data represent the number of days absent per year in a population of six employees of a small company:
1 3 6 7 9 10
a. Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Compare the mean of all the samples means and also compute the population mean. Are they equal? What is the property called?
Sampling Distribution of the Mean for n=2
Sample Number Outcome Sample Mean X
1 1.3 X=2
2 1.6 X=3.5
3 1.7 X=4
4 1.9 X=5
5 1.1 X=5.5
6 3.6 X=4.5
7 3.7 X=5
8 3.9 X=6
9 3.1 X=6.5
10 6.7 X=6.5
11 6.9 X=7.5
12 6.1 X=8
13 7.9 X=8
14 7.1 X=8.5
15 9.1 X=9.5
Total X=90
Mean of All possible Sample Means:
X=90/15=6
Mean of All Population Elements:
(1+3+6+7+9+10)/6=6
Both mean are equal to 6, this property is called Un-Biasedness.
b. Repeat (a) for all the sampling distribution of the mean in (a) and (b) . Which sampling distribution has less variability? Why?
c. Assuming that you sample with replacement, repeat (a) through (c) and compare the results. Which sampling distribution have the least variability - those in (a) or (b) ? Why?
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