List all samples of size 3 and compute the mean of each samp

List all samples of size 3, and compute the mean of each sample. (Round sample means to 2 decimal places.)

Compute the mean of the distribution of sample means and the population mean. (Round your answers to 1 decimal place.)

Solution

list of sample of size 3

(1,1,4) mean = 2

(1,1,5) mean = 2.33

(1,1,6) mean = 2.67

(1,4,5) mean = 3.33

(1,4,6) mean = 3.67

(1,5,6) mean = 4

(1,4,5) mean = 3.33

(1,4,6) mean = 3.67

(1,5,6) mean = 4

(4,5,6) mean = 5

so there are 10 possible sample of size 3

Population mean = 17/5 = 3.4

Mean of the distribution of sample mean = mean of all the sample means = 34/10 = 3.4

So Mean of the distribution of sample mean is same as population mean