HW 4-1 Problem (Small Population/Sample): Suppose there is a population of 6 peo

Question

HW 4-1 Problem (Small Population/Sample): Suppose there is a population of 6 people on a sovereign island and that it is a law on their island that subjects of study must be paid $20,000 per question. A researcher is hired to study the fish eating habits of the islanders and she only has a budget of S60,001 (the extra dollar will buy her lunch, fish of course, while she is there). She will take a SRS of 3 inhabitants. You are the monarch of the island and so know the eating habits of the islanders, as is given below: Islander A Barb Carl Darlene Earl Fran Fish week 35 21 21 16 30 a) Find the population mean for the number of fish eaten per week b all of the possible samples of size three that don't include any islander more than once) and find the sample mean for each sample. c) Find the distribution of the sample mean, r (the first probability is provided for y 15 16.7 18 19.3 19.7 21.3 22.3 24 24.3 25.7 27 28.7 (i) l 0.10

Explanation / Answer

a) Population mean, µ = (35+21+21+16+30+8)/6 = 131/6 = 21.833

b)

(Al, Barb, Carl) 77/3 = 25.7
(Al, Barb, Darlene) 24
(Al, Barb, Earl) 86/3 = 28.7
(Al, Barb, Fran) 64/3 = 21.3
(Al, Carl, Darlene) 24
(Al, Carl, Earl) 86/3 = 28.7
(Al, Carl, Fran) 64/3 = 21.3
(Al, Darlene, Earl) 27
(Al, Darlene, Fran) 59/3 = 19.7
(Al, Earl, Fran) 73/3 = 24.3
(Barb, Carl, Darlene) 58/3 = 19.3
(Barb, Carl, Earl) 24
(Barb, Carl, Fran) 50/3 = 16.7
(Barb, Darlene, Earl) 67/3 = 22.3
(Barb, Darlene, Fran) 15
(Barb, Earl, Fran) 59/3 = 19.7
(Carl, Darlene, Earl) 67/3 = 22.3
(Carl, Darlene, Fran) 15
(Carl, Earl, Fran) 59/3 = 19.7
(Darlene, Earl, Fran) 18

c)

d) µx = 15*0.1 + 16.7*0.05 + 18*0.05 + 19.3*0.05 + 19.7*0.15 + 21.3*0.1 + 22.3*0.1 + 24*0.15 + 24.3*0.5 + 25.7*0.05 + 27*0.05 + 28.7*0.1 = 21.835

x 15 16.7 18 19.3 19.7 21.3 22.3 24 24.3 25.7 27 28.7 P(X=x) 0.1 0.05 0.05 0.05 0.15 0.1 0.1 0.15 0.05 0.05 0.05 0.1

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