Q1- A population consists of three values: 3, 6, and 9.
a) Draw all possible samples with replacement of size 3.
b) Take the mean of each sample.
c) Make a sampling distribution of the sample mean.
d) Find the mean and standard deviation of the sampling distribution of the sample mean.
e) Compute the mean and standard deviation of the population.
f) Verify the results.
Q2- A population consists of 3, 6, 9, 12, and 15.
(i) Calculate the sample means for all possible random samples of size 3 that can be drawn from this population without replacement.
(ii) Verify the results.
Q3- A population consists of six numbers: 3, 6, 9, 12, 15, and 18.
Consider all possible samples of size three numbers, which can be drawn without replacement from this population. Find:
(i) The mean of the population.
(ii) The standard deviation of the population.
(iii) The mean of the "sampling distribution" of the mean.
(iv) The "standard error".
Q4- Draw all possible samples of size 3 with replacement from the population 3 and 9, then show that:
(i) Population mean = mean of sample's mean.
(ii) Standard error = Pop. S.D/n.