Question: Consider a finite population of size N=5 whose members are 3, 5, 7, 9 and 11.

(a) How many different samples of size n=2 can be drawn from this population without replacement?

(b) How many different samples of size n=2 can be drawn from this population with replacement?

(c) Considering all samples of size n=2 from this population without replacement, construct a sampling distribution of the mean ( \(\bar{X}\) ).

(d) Find the mean p and the variance \({{\sigma }^{2}}\) of the given population

(e) Find \({{\mu }_{{\bar{X}}}}\) and \({{\sigma }_{{\bar{X}}}}\); from the sampling distribution found in part (c) above

(f) Verify the formula \({{\sigma }_{{\bar{X}}}}=\frac{\sigma }{\sqrt{n}}\sqrt{\frac{N-n}{N-1}}\)