Math 311-01
The First Exam
Name: _____________
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___________
All pertinent work must be shown clearly and completely.
Complete English sentences should be used for all “short-answer” type questions.
Regardless of the final answer, credit will not be given for unclear or incorrect work.
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___________________________________________________________________________________________
Go to http://www.cwu.edu/~englundt/Data.htm and download the exam1 data set (exam1.mpj)
1.
Mrs. Clark belongs to an age/body-type group for which the mean weight is 112 pounds with a standard deviation of
11 pounds.
Mr. Clark belongs to an age/body-type group for which the mean weight is 163 pounds with a standard deviation of
18 pounds.
Mrs. Clark weighs 132 pounds and Mr. Clark weighs 193 pounds.
a. (7 points) What weight do 70% of the people in Mrs. Clark’s age/body-type group weigh more than?
b.
(7 points) What percentage of the people in Mr. Clark’s age/body-type group weigh less than him?
c.
(7 points) Which of the two Clarks is relatively more overweight compared to his/her age/body-type
group? That is, which is relatively further from the mean of his/her group? Justify your answer.
2.
81
94
91
76
91
53
82
74
Based upon 1997 figures, the following are 110 “waiting times” (in minutes) between eruptions of the Old Faithful
Geyser in Yellowstone National Park. These times are also recorded in the Minitab worksheet.
83
89
80
69
83
83
89
98
a.
3.
94
35
83
78
67
62
76
94
73
80
91
42
85
107
55
82
78
74
89
76
60
60
98
82
94
91
82
82
65
85
74
73
89
118
82
69
69
89
89
83
105
60
82
92
98
112
80
64
73
65
40
69
80
82
56
69
82
71
87
85
83
85
94
80
60
80
98
51
78
73
83
69
71
91
67
73
33
82
78
73
73
73
74
87
65
74
74
108
87
83
73
67
64
80
(10 points) Describe the data. Include the 5-number summary, the mean, the standard deviation, the
distribution, the spread, etc. Include any and all numerical or graphical summaries you feel are appropriate.
DO NOT simply list a series of numbers. Explain your findings.
The booming economy of the 1990’s created many new billionaires. The 1999 Forbes 400 ranks the 400 wealthiest
people in the United States. The top 15 billionaires on this list are described in the following table. The data in this
table can also be found in the Minitab worksheet.
Name:
Age: Net Worth ($ millions)
Gates, William
Allen, Paul
Buffett, Warren
Ballmer, Steven
Dell, Michael
Walton, Jim
Walton, Helen
Walton, Alice
43
40
69
43
34
51
80
50
85000
40000
31000
23000
20000
17300
17000
16900
Name:
Walton, John
Walton, Robson
Moore, Gordon
Ellison, Lawrence
Anschutz, Philip
Kluge, John
Anthony, Barbara
Age:
53
55
70
55
59
85
76
Net Worth ($ millions)
16800
16600
15000
13000
11000
11000
9700
a.
(5 points) Construct a scatterplot of these data. Include this graph with your exam. What does the plot
suggest about the relationship between the age and the net worth of billionaires?
b.
(5 points) Find the coefficient of correlation and explain what it tells you about the relationship between
age and net worth.
4.
(12 points) Because of the recent electricity crisis in California, the government and the utility companies have
subjected the citizens of California to a media campaign/onslaught in hopes of reducing their electricity usage. To
measure the effectiveness of their media blitz, they compiled the energy used (in kilowatt hours) in 20 homes both
one month before and one month after the campaign began. What do the data show about the effect of the
campaign? Be specific, using (only) the language and analysis tools we have learned. Use every graphical and
numerical summary that is appropriate and that we discussed in class to justify your claim.
The data recorded below are also in the Minitab worksheet.
Before the
campaign
After the
campaign
380
283
361
487
321
349
447
407
366
402
383
427
356
480
375
420
356
350
434
477
410
384
403
392
329
316
393
430
399
325
426
339
345
360
406
410
465
431
318
326
5.
Delbert Yankandpull has noticed that there appears to be a relation between Y, the number of otter haunch
sandwiches that his sweetheart, Bewfeena Twinklepuckey, eats for dinner, and X, the number of country western
songs that she sings to him that evening. He has observed the following data over the course of several truly
memorable evenings (which are, of course, also recorded in the Minitab worksheet):
X
Y
6
2
7
3
9
4
4
2
3
1
1
0
5
2
a.
(3 points) If Delbert is interested in predicting the number of country western songs she’ll serenade him
with, which variable is the explanatory variable and which is the response variable?
b.
(5 points) Describe the strength of the association of these variables using the appropriate quantifications.
c.
(3 points) Find the equation of the regression line for this data.
d.
(4 points) What does the value of r2 tell the informed viewer?
e.
(4 points) If Bewfeena ate 12 otter haunch sandwiches for dinner, what value would you predict for the
number of songs she’ll sing that night?
f.
(3 points) The prediction you just made is hazardous because: