Answer to Question #183937 in Statistics and Probability for Angel Loterte

Question

onsider the population consisting of the values (1, 3, 8)

i. List all the possible samples of size 2 with replacement.

ii. Compute the mean of each sample.

iii. Identify the probability of each sample.

iv. Compute the mean of the sampling distribution of the means.

v. Compute the population mean.

vi. Compare the population mean with the mean of the sampling distribution of mean

Answer 1

i.

ii.

$Mean \; of \; each \; sample = \frac{1st \;value + 2nd \;value}{2}$

iii.

$P(X=x) = \frac{1}{6}$

iv.

The mean of the sampling distribution of the means $= \frac{2+4.5+2+5.5+4.5+5.5}{6} = 4$

v.

The population mean

$\mu = \frac{1+3+8}{3}=4$

vi. The population mean is equal to the mean of the sampling distribution of mean.