Question 283898: A population consists of the following five values: 2,2,4,4,and 8.
a. list all samples of size 2, and compute the mean of each sample.
b. Compute the mean of the disbribution of sample means and the population mean. compare the two values.
c. Compare the dispersion in the population with that of the sample mean.
This chapter of my homework was not explained to me. I don't know where to start. I understand the mean and population formula, but I don't understand how to put it all together. If you can help, that would be great.
Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A population consists of the following five values: 2,2,4,4,and 8.
a. list all samples of size 2, and compute the mean of each sample.
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Using the 1st "2":
2,2: mean = 2
2,4: mean = 3
2,4: mean = 3
2,8: mean = 5
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Using the 2nd "2":
2,2: mean = 2
2,4: mean = 3
2,4: mean = 3
2,8: mean = 5
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Using the 1st "4":
4,2: = 3
4,2: = 38,2
4,4: = 4
4,8: = 6
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Using the 2nd "4:
4,2: = 3
4,2: = 3
4,4: = 4
4,8: = 6
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Using the "8":
8,2: = 5
8,2: = 5
8,4: = 6
8,4: = 6
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b. Compute the mean of the disbribution of sample means
Find the mean of {2,3,3,5,2,3,3,5,3,3,4,6,3,3,4,6,5,5,6,6}
= (13+13+16+16+22)/20 = (26+32+22)/20 = 80/20 = 4
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compute the population mean
Find the mean of {2,2,4,4,and 8} = 20/5 = 4
. compare the two values.
The mean of the sample means is the same as the mean of the population.
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c. Compare the dispersion in the population with that of the sample mean.
Range of the population is 8-2 = 6
Range of the sample means is 6-2 = 4
The sample means are less dispersed than the population.
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Cheers,
Stan H.
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