Question 1129763: 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. Compute the mean of all the sample means and also compute the population mean. Are they equal? What is this property called?
What I have tried using: Since the distribution is unknown, I thought of applying Central Limit Theorem (CLT). However, n < 30 which is too small to use CLT. Can I still assume that the distribution is normal even though the question does not mention it?
b. Repeat (a) for all possible samples of n = 3.
c. Compare the shape of the sampling distribution of the mean in (a) and (b). Which sampling distribution has less variability? Why?
d. Assuming that you sample with replacement, repeat (a) through (c) and compare the results. Which sampling distributions have the least variability—those in (a) or (b)? Why?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The mean of the mean of the samples is the same as the sample mean, or 6.
The sample means of n=2 are
1-3
1-6
1-7
1-9
1-10
3-1
3-6
3-7
3-9
3-10 etc.
add all those means up and divide by their number, which is 30, to get the mean of the sampling distribution.
With n=3 samples, you will get the same mean.
The variability will be less the larger the sample size. They will look roughly normal. Don't worry about the CLT.
|
|
|
