A finite population consists of four elements: 6, 1, 4, 2. (a) How many differen

Question

A finite population consists of four elements: 6, 1, 4, 2.

(a) How many different samples of size n = 2 can be selected from this population if you sample without replacement? (Sampling is said to be without replacement if an element cannot be selected twice for the same sample.) samples

(b) List the possible samples of size n = 2. (Enter your answers as a comma-separated list. Enter samples in the form (a, b), with the smaller value first.)

(c) Compute the sample mean for each of the samples given in part (b). (Enter your answers as a comma-separated list.)

(d) Find the sampling distribution of x.

p(x) = 1 2 for x = 1, 2

p(x) = 1 3 for all values of x

p(x) = 1 6 for all values of x

p(x) = 1 6 for x = 1, 2, 3, 4, 5, 6

p(x) = 1 2 for x = 1, 2, 3, 4, 5, 6

(e) If all four population values are equally likely, calculate the value of the population mean . (Enter your answer to two decimal places.)
= 6

Do any of the samples listed in part (b) produce a value of x exactly equal to ?

Yes, sample 1 produces a value of x equal to . Yes, sample 2 produces a value of x equal to .    

Yes, sample 3 produces a value of x equal to .

Yes, sample 4 produces a value of x equal to . Yes, sample 5 produces a value of x equal to .

Yes, sample 6 produces a value of x equal to .

None of the samples produce a value of x equal to .

Explanation / Answer

a. No. of different samples of size 2 is 4C2=6

b. Different samples: (1,2), (1,4), (1,6),(2,4),(2,6),(4,6)

c. The respective mean is (1.5, 2.5, 3.5, 3, 4, 5)

d. Please define x in the comment and I will explain.

e. Related to part d, so please clear the "x" here.

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