Question

THE FOLLOWING ARE THE HEIGHTS OF FOUR STUDENTS IN CENTIMETERS. SUPPOSE SAMPLES SIZE 2 ARE TAKEN FROM THIS POPULATION OF FOUR STUDENTS.

STUDENTS HEIGHT (in cm)

CARDO 125

ALYANA 120

JOAQUIN 130

FLORA 110

a. how many samples are possible?

b. construct the sampling distribution of the sample means

c. construct the histogram of the sampling distribuyion of the sample means

Answer 1

a. $C^2_4=\frac{4!}{2!2!}=6$

b.m (125,120)=(125+120)/2=122.5

m(125,130)=(125+130)/2=127.5

m(125,110)=(125+110)/2=117.5

m(120,130)=(120+130)/2=125

m(120,110)=(120+110)/2=115

m(130,110)=(130+110)/2=120

Frequency

F(122.5)=F(127.5)=F(117.5)=F(125)=F(115)=F(120)=1

Probability

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

P(122.5)=P(127.5)=P(117.5)=P(125)=P(115)=P(120)=1/6

$E(x)=\sum Px=1/6(122.5+127.5+117.5+125+115+120)=121.25$

$\sigma^2=\sum Px^2-(\sum Px)^2=1/6(15006.25+16256.25+13806.25+15625+13225+14400)-14701.56=18.23$

c.