A finite population consists of four elements: 6, 1, 5, 3 (a) How many different

Question

A finite population consists of four elements: 6, 1, 5, 3 (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 (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 arn WI 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.) (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.)

Explanation / Answer

a)

There are 4 elements, and we take samples of 2.

Hence, there are 4C2 = 6 samples. [ANSWER, 6]

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b)

Hence, the samples are

(1,3), (1,5), (1,6), (3,5), (3,6), (5,6) [ANSWER]

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c)

Hence, their means are

2, 3, 3.5, 4, 4.5, 5.5 [ANSWER]

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E)
Getting the mean,

u = (6+1+5+3)/4 = 3.75 [ANSWER]

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