quiz4sols

# quiz4sols - So they are the same b SD for box 1=(29 –-1...

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Quiz 4 solution: 1. a) The first option is better. In order to win, we hope the chance error in percentage for both options to be larger than 3.3/40=6.6/80. Fewer draws have larger chance error in percentage. So option 1 is better. b) The first option is better. In order to win, we hope the chance error in absolute terms for both options to be less than 5. Fewer draws have less chance error in absolute terms. So option 1 is better. 2. a) expected net gain for option i)=(29 – 35)/36*60= -\$10 expected net gain for option ii)=(4*6 – 30)/36*60= -\$10
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Unformatted text preview: So they are the same b) SD for box 1= (29 – (-1)) sqrt(1/36*35/36)= 4.93 SD for box 2=(4 – (-1)) sqrt(6/36*30/36)= 1.86 SE for option 1 = 4.93 * sqrt(60)=38.19 SE for option 2 = 1.86 * sqrt(60)=14.41 Option 1 has a larger SE, so it is easier to come out ahead with. 3. AV of box = (1+3-1)/5=0.6 Expected value for sum=0.6*100=60 SD of box=sqrt((0.4^2+2.4^2+(-1.6)^2+(-0.6)^2+(-0.6)^2)/5)=1.356 SE for sum = 1.356*sqrt(100)=13.56 The sum of the odd numbers drawn should be around 60, give or take 13.56...
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