Answer to Question #317890 in Statistics and Probability for Aswani

Question

If a finite population has four elements: 6, 1, 3, 2.

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

(b) List all possible samples of size n = 2.

(c) Compute the sample mean for each of the samples given in part b.

(d) Find the sampling distribution of and draw the histogram.

(e) Compute standard error.

(f) If all four population values are equally likely, calculate the value of the population mean . Do any of the samples listed in part (b) produce a value of exactly equal to mean

Answer 1

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

$C(4,2)=6$

(b) List all possible samples of size n = 2.

$(6,1),(6,3),(6,2),(1,3),(1,2),(3,2)$

(c) Compute the sample mean for each of the samples given in part b.

(d) Find the sampling distribution of and draw the histogram.

$P(X=3.5)=P(X=4.5)=P(X=4)=P(X=2)=P(X=1.5)=P(X=2.5)=\frac{1}{6}$

(e) Compute standard error.

$\sigma=\sqrt{10.1734-3^2}=\sqrt{1.1734}=1.0832$

S.E $=\frac{\sigma}{\sqrt{n}}=\frac{1.0832}{6}=0.18$

(f) If all four population values are equally likely, calculate the value of the population mean . Do any of the samples listed in part (b) produce a value of exactly equal to mean

Population mean $=\frac{6+1+3+2}{4}=3$

None of the sample means produce an exact mean equal to the population mean.