Answers to the Second Midterm Purple Form
1. Answer is 12.6 to 13.4 hours. If you chose to
write 13/24 as the percentage of hours, it was OK only
if you contined and calculated the SE correctly (SE of
a percentage). Otherwise, the solution is:
13 hours + or - (2 * ((root(16) * .08)/16))
2. C -- accuracy is determined by sample size not by
population size. See chapter 20.
3. D
4. it would be
60% + or - 2.333% (2.333% is the answer from #3)
5. The newspaper is. Why? Because it uses a probability method
to generate a representative sample of the US population. The TV
method is biased -- selection bias and possibly reponse bias.
6. Here, the population is known and you're being asked about the
chance of seeing a particular sample outcome -- specifically
between 16% and 20%.
Need a Z score
Z = 16% - 15%
------------------------------------- = .336 or about .30
(root 144) * (root .15 * .85)
------------------------ * 100
144
Z = 20% - 15%
------------------------------------- = 1.68 or about 1.65
(root 144) * (root .15 * .85)
------------------------ * 100
144
The area associated with a Z = 1.65 is 90.11%
The area associated with a Z = .3 is 23.58%
Take the difference in this case and divide by 2 to give
33.265%
7. Box Average = -.2 so the expected value is 100 x -.2 = -$20
Solution for box average :
(+10 * .1) + (-6 * .2) + (0 * .7) = -.2
SD of the box -- this is trickier. Remember the formula from
chapter 4? The standard deviation is the average deviation
of each outcome from the average. So we know the average is -.2
the possible outcomes are
0 (if you picked a red, brown, green, blue)
+10 (if you picked an orange one)
-6 (if you picked a yellow one)
70% of the M&Ms are worth zero dolalrs
10% are worth +$10
20% are worth -$6
So, treat the M&M outcomes like a list of numbers, that is:
0, 0, 0, 0, 0, 0, 0, +10, -6, -6
The SD of this list is $4.1424
So the SE of the sum is root(100) * 4.1424 or $41.425
8. You lost $114, this is -114 and you were only expecting
to lose $20 (-20). Need to calculate Z to find the chance
of seeing this kind of outcome:
Z = -114 - (-20)
------------
41.425
= -2.27, round down to -2.25, the area to left of -2.25 is
1.22%. So there was about a 1.22% chance of losing $114 or
more.