A finite population consists of four elements: 5, 1, 4, 3. (a) How many differen

Question

A finite population consists of four elements: 5, 1, 4, 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 element cannot be selected twice for the same sample.) (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. (e) If all four population values are equally likely, calculate the value of the population mean . (Enter your answer to two decimal places.)

Explanation / Answer

Four elements in the population = 5,1,4,3

Number of ways to choose 2 out of those 4 without replacement = 4C2 = 6

Listing them we get : [ (1,4); (1,3); (1,5); (4,3); (3,5); (4,5) ]

Mean for each sample is (2.5 , 2, 3, 3.5, 4 , 4.5 )

for remaining  x - must be explained as to what it actually is, otherwise there are no possible answers.

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