Answer to Question #332105 in Statistics and Probability for josh

Question

The Following are the heights of four students in centimeters. Suppose samples of size 2 ae taken from this population of four students.

cardo-125 cm

alyana-120cm

joaquin-130 cm

flora-110 cm​

a. How many samples are possible? List them and compute the mean of each sample?

b. Construct the sampling distribution of the sample means

c. Construct the histogram of the sampling distribution of the sample means

Answer 1

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

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

b. Frequencies

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

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

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

c.