Answers to the Second Midterm Orange 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(49) * .8 /49))
2. C -- accuracy is determined by sample size not by
population size. See chapter 20.
3. C
4. it would be
60% + or - 2.33% (the answer from #3)
5. Box Average = -.4 so the expected value is 100 x -.4 = -$40
Solution for box average :
(-5 * .2) + (+6 * .1) + (0 * .7) = -.4
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 -.4
the possible outcomes are
0 (if you picked a red, brown, green blue)
-5 (if you picked a yellow one)
+6 (if you picked an orange one)
70% of the M&Ms are worth zero dolalrs
20% are worth -$5
10% are worth +$6
So, treat the M&M outcomes like a list of numbers, that is:
0, 0, 0, 0, 0, 0, 0, -5, -5, +6
The SD of this list is $2.9052
So the SE of the sum is root(100) * 2.9052 = $29.052
6. You lost $103, this is -103 and you were only expecting
to lose $40 (-40). Need to calculate Z to find the chance
of seeing this kind of outcome:
Z = -103 - (-40)
------------
29.052
= -2.17, round down to -2.15, the area to left of -2.15 is
1.58%. So there was about a 1.6% chance of losing $103 or
more.
7. 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.
8. 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%