Instructions: Answer all questions and show all work.

Suppose we have a population of size N = 3 units:

U = {y1, y2, y3} = {2, 3, 4}.

The values for y are

y1 = 2, y2 = 3, y3 = 4.

The population standard deviation is (statistician does not know this) and .

a.) How many possible samples of size 2, n = 2, can be obtained under sampling without replacement and not considering order of the draws (hint: NCn = ).

b.)Obtain all the samples indicated in a.

c.) For the population of samples obtained in b, compute the sample mean for each corresponding sample (this is a population of sample means).

d.)Compute the standard error of the mean under sampling without replacement and not considering order of the draws,

=

e.)Using the critical values of standard normal approximation of ±Z = ±0.967 as the critical value compute the Margin of Error (MoE).

f.)Construct the 66.67% confidence interval for the mean for each sample obtained

in c and report the to two decimals places (hint: )

g.)Does the nominal confidence level of 66.67% coincide with the observed percent of confidence intervals containing the population mean?

Hint

You may elect to construct a table with the following column headings with rows.

# Sample Mean MoE = Interval Contains