Math 151 Exam 2 Oct. 10, 2008 NAME_ Comments___
Closed book, one sheet of notes. Get Normal Tables from me. Please put your name on the sign-in sheet; if
you go somewhere else to work, write down where you are going. Please stay in the building.
Do your work on these pages or attach sheets if necessary. Show your work for full or partial credit. Corrected 10/15,11am
prob# 1 2 3reading 3Normal 4 5 6 Scat+ Normal
100 4 23 6 19 30 9 9 100% 100% 9 6
possible 100 4 23 6 19 30 9 9 75 19 9 12
max 96 4 23 6 19 29 9 9 95% 100% 8 558999
Q3 87 4 22 6 19 26 9 9 87% 99% 8 0023333334
Med 83 2 21 6 17 23 9 9 83% 87% 7 688
Q1 78 0 19 4 14 21 7 6 76% 75% 7 4
min 53 0 13 0 1 14 5 3 1 0 low 59, 55, 53
Quite good overall!
Some substantial improvements, some drops. Please come and see me if you’re near the bottom!
I broke problem 3 into part a, the Reading, and the rest, the Normal distribution. The other problems were
all on scatterplots plus. Scores broken down for the two parts.
Only a few problem-specific comments. Complete Solutions
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1) From Are Bad Times Healthy, this Tuesday (NY Times Science Times, Oct 7, ’08). ― Dr Ruhm found that death rates
declined sharply in the 1974 and 1982 recessions, and increased in the economic recovery of the 1980s. An increase
of one percentage point in state unemployment rates ..[corresponded to] a 0.5 percentage point decline in the
death rate‖.
a) What kind of analysis would produce these results? Linear Regression, Death rate on unemployment rate.
b) What is the 0.5 (really –0.5 since it’s a decline)? Slope of the line
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2) Month-by-month data on the production of cottage cheese (millions of pounds) and ice cream (millions of gallons)
for a recent year are graphed here. Both are ways to ―store‖ milk A
for longer than fresh milk (but shorter than hard cheese or dried milk.) 80.0 Jl
a) In which month was more cottage cheese produced? A
Au
A
September (Sp) or October (Oc) Jn
b) Describe the graph using these criteria (you can circle
choices) People ―see‖ different things—I see 3 clusters. 70.0 A
Sp A
Oddest thing is the blank space up the diagonal. My
icecre am
c) Scatter: Below is a list of potential values for the A
A
Ap
correlation coefficient r of this data set. Oc
A
Mr
60.0
i) Mark with an A the value you think is closest to the
true r. Surprisingly, it’s actually .61. Even with the blank
space up the middle, it has a lot of ―linear direction‖ A
A Ja A
De Fe
Values for r: –1.5 –1 –.96 –.61
–.15 0 .15 .61 .96 1 2 50.0 A
No
70.0 75.0 80.0 85.0
d) The time of year is a likely lurking variable here, so the points have been
labeled with the months. (Connecting the dots in time sequence is interesting.) Use this cottagecheese
information and give a detailed description of the pattern for someone who can't see the graph, in terms of ice cream
and cottage cheese production.
Both Very seasonal, (low in cold months). Ice cream is very temperature dependent ;-). But cottage cheese not higher
in hottest weather; highest in May (spring-fall food?)
More detail in solutions.
p. 2
4) This is a graph for 60 American cities of mean A
January temperature (Fo) on latitude (higher 65.0
latitude means farther north)
60.0
(Both temperature and latitude are measured in "degrees")
55.0 A A
A A
Summary statistics:
R2 = 0.73 50.0 A
A
Jan. Temp (F)
A
AA
JanTemp = 118.14 – 2.15 lat 45.0
A
A
(that is, y 11814 2.15x )
. 40.0 A
A
A
A
B
B
35.0 A A
AA AAA
a) What is the correlation coefficient for this A A
A
A
A
A
AA AA A
data set? 30.0 A A A A
AA A
A AA A
A
A
25.0 A
AA A
A A
It’s a negative relationship, looking at the graph, so A
20.0
you have to take the NEGATIVE square root of
R2 = 0.73 15.0
A
10.0
25.00 30.00 35.00 40.00 45.00
e) Miami, FL is the city by itself in the upper left corner. Circle the choice that will North
be true if we remove this outlier: latitude
The correlation will get closer to 0 (weaker) // stay the same // get farther from 0 (stronger).
f) The two outliers on the right (B) are Portland, OR, and Seattle, WA (Seattle is the furthest north of all these cities!)
For each statement, circle the choice that will be true if we remove these two outliers.
i) The regression line will get flatter // will not change its slope very much // will get steeper
ii) The R2 value will get smaller (closer to 0) //stay the same// get larger (closer to 1).
Aside: What’s special about Portland and Seattle that make them warmer than expected in the coldest months?
Wasilla Alaska. 61.6 North Mean Jan, 08 = 11.1 predicted 118.44-132.44 = –14.3
http://weather.alaskatech.org/
Cold but not as cold as predicted! Where is it?