How many different samples of size n 2 can be selected from

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

Please help, thank you!

the population contains four elements: 6,2,5,4

the sample size is n=2. the sample is drawn by without replacement.

so from 4 elements we can select 2 elements in ⁴C₂ ways.

a) number of different samples: ⁴C₂=6 [answer]

b)the possible samples are-

(2,4) (2,5) (2,6) (4,5) (4,6) (5,6)

c) the sample means are [ for (a,b) xbar=(a+b)/2 ]

for (2,4) xbar=3

(2,5) xbar=3.5

(2,6) xbar=4

(4,5) xbar=4.5

(4,6) xbar=5

(5,6) xbar=5.5

d) as the sample is drawn using simple random sampling without replacement. all the samples are equally likely.

hence the sampling distribution of xbar is

option d) p(xbar)=1/6 for all values of xbar=

d) the correct histogram is option b) [top right]

because it has bars for all the values of xbar=3, 3.5, 4, 4.5, 5, 5.5 with equal length.

e) population mean mu= (6+2+4+5)/4=4.25

f) none of the samples produce a value of xbar equal to mu.