5 A population consists of the values 1 2 5 a List all possi

5. A population consists of the values 1, 2, 5. a. List all possible all of the possible samples (with replacement) of size 2 along with the sample means and their individual probabilities. b. Find the mean and standard deviation of the sampling distribution of g . 6. A population consists of the values 3, 7, 2, 9, 11, 16, 20, 23, 14, 15. Take a sample of size four from this population. Find the mean and standard deviation of the sampling distribution of X.

Solution

5.a) popltn = 1 ,3 ,5..
i) (1,3).......sample mean = 2...
ii) (1,5)....sample mean =3.....
iii) (3,5)....sample mean =4.....
individual prob.of 1 unit = 1/3...individual prob. for 1 sample=2/3..

(b) i)mean = 2...s.d = s.d of x =1
ii)mean=3..s.d =2
(iii)mean=4 , s.d=1 (approx)

(6) see a random no. table and choose 4 samples!
I took the 1st row of random no. table..and my sample =11,16,7,5....

mean = 9.75.. s.d = 4.856267.......