Thread: Standard Error (probability help)

Hi everyone. I've been working on this assignment for a whole day. Not sure if all my answers below are correct. Can someone help please confirm my answers? Especially for the standard error ones since I'm quite confused with all these formulas... I got my formulas from the textbook:

http://i50.tinypic.com/kcytk2.png

Thank you in advance! Sorry for the lengthy post!

PS- 5.39921 is the SD of the box.

A box contains twelve tickets labeled with numbers. The number on the tickets are

-10, -7, -5, -5, -4, -3, -2, -1, 0, 3, 4, 10.

1. The expected value of the sample sum of the ticket labels in 13 independent random draws with replacement from the box is
-21.6666667
(((-10) - 7 - 5 - 5 - 4 - 3 - 2 - 1 + 0 + 3 + 4 + 10) / 12) * 13 = -21.6666667


2. The standard error of the sample sum of the ticket labels in 13 independent random draws with replacement from the box is
19.4671285
sqrt(13) * 5.39921 = 19.4671285


3. The expected value of the sample mean of the ticket labels in 13 independent random draws with replacement from the box is
-1.6666666666666666666666666666667
(((-10) - 7 - 5 - 5 - 4 - 3 - 2 - 1 + 0 + 3 + 4 + 10) / 12) = -1.66666667


4. The standard error of the sample mean of the ticket labels in 13 independent random draws with replacement from the box is
1.55861767
5.39921/(12)½ = 1.55861767


5. The expected value of the sample mean of the ticket labels in a simple random sample of 12 tickets from the box is
-1.6666666666666666666666666666667
(((-10) - 7 - 5 - 5 - 4 - 3 - 2 - 1 + 0 + 3 + 4 + 10) / 12) = -1.66666667


6. The standard error of the sample mean of the ticket labels in a simple random sample of 12 tickets from the box is
18.7034121
(12−12)^(1 / 2)/(12−1)^(1 / 2) * (12^(1 / 2)) * 5.39921 = 18.7034

Help please !

4. The standard error of the sample mean of the ticket labels in 13 independent random draws with replacement from the box is
1.55861767
5.39921/(12)½ = 1.55861767

Shouldn't this be 5.39921/(13)^1/2 since n is 13?

6. The standard error of the sample mean of the ticket labels in a simple random sample of 12 tickets from the box is
18.7034121
(12−12)^(1 / 2)/(12−1)^(1 / 2) * (12^(1 / 2)) * 5.39921 = 18.7034

Doesn't this = 0?

The rest seem correct to me, assuming that the SD is correct! :]