Answers to the Second Midterm Blue Form
1. A -- accuracy is determined by sample size not by
population size. See chapter 20.
2. 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.
3. D
4. it would be
75% + or - 4.558% (2*the answer from #3)
5. Answer is 12.8 to 13.2 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(36) * .5)/36))
6. Box Average = -.6 so the expected value is 100 x -.6 = -$60
Solution for box average :
(-5 * .3) + (+9 * .1) + (0 * .6) = -.6
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, green, yellow, orange)
-5 (if you picked a brown one)
+9 (if you picked a blue one)
60% of the M&Ms are worth zero dolalrs
30% are worth -$5
10% are worth +$9
So, treat the M&M outcomes like a list of numbers, that is:
0, 0, 0, 0, 0, 0, -5, -5, -5, +9
The SD of this list is $3.9038
So the SE of the sum is root(100) * 3.9038 = $39.038
7. You lost $158, this is -158 and you were only expecting
to lose $60 (-60). Need to calculate Z to find the chance
of seeing this kind of outcome:
Z = -158 - (-60)
------------
39.038
= -2.51, round down to -2.5, the area to left of -2.5 is
.62%. So there was about a .6% or 6 in 1000 chance of losing $158 or
more.
8. Here, the population is known and you're being asked about the
chance of seeing a particular sample outcome -- specifically
between 5% and 9%.
Need a Z score
Z = 9% - 10%
------------------------------------- = -.366 or about -.35
(root 121) * (root .10 * .90)
------------------------ * 100
121
Z = 5% - 10%
------------------------------------- = -1.83 or about -1.80
(root 121) * (root .10 * .90)
------------------------ * 100
121
The area associated with a Z = -1.80 is 92.81%
The area associated with a Z = -.35 is 27.37%
Take the difference in this case and divide by 2 to give
32.72%