Question

List all possible samples of size n=3, with replacement, from the population (1,3,5). Calculate the mean...

List all possible samples of size n=3, with replacement, from the population (1,3,5). Calculate the mean of each sample. Construct a probability distribution of the sample means and compute the mean, variance, and standard deviation of the sample means and compare to the mean, variance, and standard deviation of the population.

0 0
Add a comment Improve this question Transcribed image text
Answer #1

for population:

x P(x) xP(x) x^2P(x)
1    1/3 0.33 0.33
3    1/3 1.00 3.00
5    1/3 1.67 8.33
total 3.00 11.67

mean =E(X)=3.00

Variance =E(X2)-(E(X))2 =11.67-32 =2.67

and standard deviation =sqrt(2.67)=1.633

for probability distribution of the sample means :

x1 x2 x3 P(x1,x2) xbar xbar*P(xbar) xbar^2*P(xbar)
1 1 1    1/27 1.000 0.037 0.037
1 1 3    1/27 1.667 0.062 0.103
1 1 5    1/27 2.333 0.086 0.202
1 3 1    1/27 1.667 0.062 0.103
1 3 3    1/27 2.333 0.086 0.202
1 3 5    1/27 3.000 0.111 0.333
1 5 1    1/27 2.333 0.086 0.202
1 5 3    1/27 3.000 0.111 0.333
1 5 5    1/27 3.667 0.136 0.498
3 1 1    1/27 1.667 0.062 0.103
3 1 3    1/27 2.333 0.086 0.202
3 1 5    1/27 3.000 0.111 0.333
3 3 1    1/27 2.333 0.086 0.202
3 3 3    1/27 3.000 0.111 0.333
3 3 5    1/27 3.667 0.136 0.498
3 5 1    1/27 3.000 0.111 0.333
3 5 3    1/27 3.667 0.136 0.498
3 5 5    1/27 4.333 0.160 0.695
5 1 1    1/27 2.333 0.086 0.202
5 1 3    1/27 3.000 0.111 0.333
5 1 5    1/27 3.667 0.136 0.498
5 3 1    1/27 3.000 0.111 0.333
5 3 3    1/27 3.667 0.136 0.498
5 3 5    1/27 4.333 0.160 0.695
5 5 1    1/27 3.667 0.136 0.498
5 5 3    1/27 4.333 0.160 0.695
5 5 5    1/27 5.000 0.185 0.926
total 3.000 9.889

mean of sampling distribution of sample means =E(Xbar)=3.00

and variance of sampling distribution of sample means =9.889-32 =0.889

and standrd deviation of sampling distribution of sample means =sqrt(0.889)=0.943

from above population mean =sampling distribution of sample means

standrd deviation of sample means =population standard deviation/sqrt(3)

variance of sample means =population variance/3

Add a comment
Know the answer?
Add Answer to:
List all possible samples of size n=3, with replacement, from the population (1,3,5). Calculate the mean...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT