Answer to Question #326595 in Statistics and Probability for Aina

Question

Random samples of size n-2 are drawn from a finite population consisting of the following numbers 5,6,7,8, and 9.

a. How many possible outcomes are there? b. List all the possible samples and the corresponding mean for each.

sample.

c. Construct the sampling distribution of the sample means.

Answer 1

$C^2_5=\frac{5!}{3!2!}=10$ samples

m(5,6)=(5+6)/2=5.5

m(5,7)=(5+7)/2=6

m(5,8)=(5+8)/2=6.5

m(5,9)=(5+9)/2=7

m(6,7)=(6+7)/2=6.5

m(6,8)=(6+8)/2=7

m(6,9)=(6+9)/2=7.5

m(7,8)=(7+8)/2=7.5

m(7,9)=(7+9)/2=8

m(8,9)=(8+9)/2=8.5

Frequency

F(5.5)=F(6)=F(8)=F(8.5)=1

F(6.5)=F(7)=F(7.5)=2

Probability $P(X)=F(x)/\sum F(x)$

P(5.5)=P(6)=P(8)=P(8.5)=1/10=0.1

P(6.5)=P(7)=P(7.5)=2/10=0.2

$E(x)=\sum P(x)x=0.1(5.5+6+8+8.5)+0.2(6.5+7.5+7)=2.8+4.2=7$

$\sigma^2=\sum P(x)x^2 - (\sum P(x)x)^2=0.1(30.25+36+64+72.25)+0.2(42.25+56.25+49)-49=20.25+29.5-49=0.75$