i just need 6,7,8, i have the rest Sampling Distributions This exercise is to be

Question

i just need 6,7,8, i have the rest

Sampling Distributions

This exercise is to be completed in a group.

For the population:          1               3               5               7               9

1. Find the mean and standard deviation.

2.Now determine how many samples of size 2 can be formed from this population of size 5, disregarding order. Use the appropriate formula.

3.List all the samples of size 2 that can be formed from this population. Be sure the list is consistent with the answer obtained from the formula. Otherwise, check your work.

4.Calculate the mean of each of the samples of size 2.

6.Create a probability distribution of all the sample means from the sample of size 2. (HINT: If you have a mean of 7 in the list of sample means and it occurs 3 times out of 10, then the probability is 0.3 for that mean value.)

7..Calculate the mean and standard deviation of that probability distribution using the appropriate formulas.

8.How do the measures of the probability distribution compare to the measures from the original population? What type of probability distribution appears to be formed? Summarize any conclusions that would be fair to draw from these results.

Explanation / Answer

6) Given population size N = 5 and n = 2

In without replacement, the possible samples 5C2 = 10 ways

The sampling distribution of mean is

The probability mass function of sample mean is

7) Mean E(X) = 2*0.1+3*0.1+4*0.2+5*0.2+6*0.2+7*0.1+8*.1 = 5

E(X2)= 22*0.1+32*0.1+42*0.2+52*0.2+62*0.2+72*0.1+82*.1 = 28

Var(X) = E(X2) - [E(X)]2 = 28 - 52 = 3

SD(X) = Sqrt(3) = 1.732

8. Original population mean = 5 which is equal to mean of sampling distribution of mean

Original population Sd = 2.828

SD of sampling distributoin of mean is 1.732 = 2.828/sqrt(2) ((N-n)/(N-1))= 1.9999 * (3/4) = 1.732

With out replacement Sampling distribution Samples 1st draw 2nd draw of mean 1 1 3 2 2 1 5 3 3 1 7 4 4 1 9 5 5 3 5 4 6 3 7 5 7 3 9 6 8 5 7 6 9 5 9 7 10 7 9 8

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