There are two options in a box model experiment: (i) One hundred draws will be m

Question

There are two options in a box model experiment:     (i) One hundred draws will be made at random with replacement from Box A : (1, 1, 5, 7, 8, 8)   (ii) Twenty-five draws will be made at random with replacement from Box B : (14, 17, 21,23,25) (a) Determine the following quantities for each box experiment. Write your answer in the following table

(b) Which box is better if the payoff is $1 for each of the following options. Show necessary calculations to support your answers (i) the sum is 550 or more, and nothing otherwise: Box _____ is better (ii) The sum is between 450 and 550, and nothing otherwise: Box ________ is better.  

BOX Average SD Expected Value(SUM) Standard E(SUM) A B

Explanation / Answer

(a) We can use R to solve this

> rm(list=ls(all=TRUE))
> x=c(1, 1, 5, 7, 8, 8)
> ######### Box A############
> yA=sample(x, 100, replace=T)
> yA
[1] 1 1 8 7 8 5 5 1 8 8 7 8 7 1 5 7 1 7 8 7 1 1 8 1 7 1 1 7 5 5 5 1 1 7 8 8 7
[38] 8 1 1 1 1 1 1 8 7 1 7 5 1 7 8 8 7 1 8 8 8 8 8 1 8 1 5 1 8 7 8 1 5 5 8 8 8
[75] 1 8 5 1 8 7 8 8 1 1 7 1 8 1 7 8 8 8 8 7 8 8 7 1 1 8
> avA=mean(yA)
> avA
[1] 5.16
> sdA=sd(yA)
> sdA
[1] 3.06403
> sA=sum(yA)
> sA
[1] 516
> seA=sdA/(sqrt(length(yA)))
> seA
[1] 0.306403
> ######### Box B############
> yB=sample(x, 25, replace=T)
> yB
[1] 8 5 5 1 8 7 8 5 5 8 5 7 1 8 1 5 8 8 8 1 8 8 8 1 1
> avB=mean(yB)
> avB
[1] 5.52
> sdB=sd(yB)
> sdB
[1] 2.859487
> sB=sum(yB)
> sB
[1] 138
> seB=sdB/(sqrt(length(yB)))
> seB
[1] 0.5718974
>

(b) Box A is better

(c) The sum is between 450 and 550, and nothing otherwise: Box A is better

BOX Average SD Expected Value(SUM) Standard E(SUM) A 5.16 3.06403 516 0.306403 B 5.52 2.859487 138 0.571897

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