In: Advanced Math
Suppose there is a class with four people in it, and their overall grades in the course are 85, 92,78, and 75.
A. Write down every possible simple random sample of grades with sample sizen= 2.
B. Write down the sample space for the means x of the samples of size n= 2.
C. Find the mean of the sampling distribution from (b).
please explain the answers
A. Simple Random Sample with Sample Size 2 means that we pick
out (randomly) any two of the four grades given us, so this would
mean that all possible simple random samples are as follows:
{85,92},{85,78},{85,75},{92,78},{92,75},{78,75}
B. The elements in the Sample Space for the means of the samples of
size n = 2 are the means of each of the six sets of numbers in part
A. That is, for the sample {85,92} we have (85+92)/2 = 88.5. So on
and so forth. Thus we have the sample space (which I've arranged in
alphabetical order): {76.5, 80, 81.5, 83.5, 85, 88.5}
C. The mean of the sampling distribution would be the mean of
the sample space we got in part B. This is
(76.5+80+81.5+83.5+85+88.5)/6 = 82.5
(To check our answer we note that the mean of our initial data, 85,
92,78, and 75 is 82.5 as well. This is because of the Central Limit
Theorem which you can check out!)
Hope this helps and clarifies! If it did, please leave a positive
response! Thanks :)