THE FIRST EXAM
MATH 311, WINTER 2004
JANUARY 25, 2005
NAME: ________________________________
_____________________________________________________________________________________________________________
 ALL PERTINENT WORK MUST BE SHOWN NEATLY AND CORRECTLY. POINTS WILL BE DEDUCTED FOR INCORRECT, MISSING, OR
UNCLEAR WORK REGARDLESS OF THE FINAL ANSWER.
 COMPLETE ENGLISH SENTENCES MUST BE GIVEN FOR ALL “SHORT ANSWER” TYPE QUESTIONS.
 DATA MAY BE OBTAINED AT HTTP://WWW.CWU.EDU/~ENGLUNDT
1. (6 points) A company produces packets of soap powder labeled "Giant Size 32 oz." The actual weight of
soap powder in a box has a normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz.
What proportion of packets are underweight (i.e., weigh less than 32 oz.)?
a.
b.
c.
d.
.0764
.2420
.7580
.9236
2. (4 points) A study is conducted to determine if one can predict the yield of a crop based on the amount of
yearly rainfall. The response variable in this study is
a.
b.
c.
d.
yield of the crop.
amount of yearly rainfall.
the experimenter.
either bushels or inches of water.
1. (4 points) The average salary of all female workers is $35,000. The average salary of all male workers is
$41,000. What must be true about the average salary of all workers?
a.
b.
c.
d.
It must be $38,000.
It must be larger than the median salary.
It could be any number between $35,000 and $41,000.
It must be larger than $38,000.
2. (4 points) Which of the following is likely to have a mean that is smaller than the median?
a. The salaries of all National Football League players.
b. The scores of students (out of 100 points) on a very easy exam on which most score perfectly, but a
few do very poorly.
c. The prices of homes in a large city.
d. The scores of students (out of 100 points) on a very difficult exam on which most score poorly, but
a few do very well.
3. A sample was taken of the salaries of 20 employees of a large company. The following is a boxplot are the
salaries (in thousands of dollars) for this year.
a. (4 points) Based on this boxplot, which of the following statements is true?
i.
ii.
iii.
iv.
The maximum salary is between 60 and 70 thousand dollars.
The minimum salary is 20 thousand dollars.
The interquartile range is about 20 thousand dollars.
The median salary is a little less than 40 thousand dollars.
b. (4 points) Based on this boxplot, which of the following statements is true?
i.
ii.
iii.
iv.
The salary distribution is fairly symmetric.
About 10 employees make more than $50,000.
Nobody makes more than $80,000.
All of the above.
c. (4 points) What does the line in the middle of the box (between 48 and 49) represent?
i.
ii.
iii.
iv.
The mean of the data.
The median of the data.
The mode of the data.
All of the above.
4. Urbano-Marquez et al. (1989) reported on strength tests for a group of 50 alcoholic men, carefully selecting
them from a larger group of alcoholic men to form a homogenous group. The total lifetime consumption of
alcohol per kilogram of body weight was determined for each person in the study (kg per kg of body
weight). The strength of the deltoid muscle in each person’s non-dominant arm was also measured (kg).
These measurements are recorded in the Minitab worksheet Exam1.MPJ
a. (5 points) Find a least-squares regression line that can be used to predict an alcoholic man’s muscular
strength from his lifetime consumption of alcohol.
Answer: ________________________________________
b. (6 points) Describe, using the appropriate quantifiers, the relationship between an alcoholic man’s
lifetime consumption of alcohol and his muscular strength.
5. (8 points) Many test preparation companies claim to be able to increase their client’s SAT scores. Below
are the SAT scores of 40 students selected at random from a group of students who took the SAT exam
twice. The first time they took the exam was before enrolling in the test prep program and the second time
was after completing the program. The scores are arranged completely randomly within the “before”
and “after” categories. They can also be found in the Minitab worksheet, exam1.MPJ.
Before
After
680
670
660
680
580
700
730
700
650
630
700
780
650
620
730
770
640
660
730
710
620
650
740
670
650
780
700
730
710
700
610
700
680
620
700
690
760
700
630
630
Use these data to assess the claims of the test prep company. Do you agree or disagree with the company’s
claim? Support your opinion statistically.
6. 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.
81
94
91
76
91
53
82
74
83
89
80
69
83
83
89
98
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
a. (3 points) What is the interquartile range of these times?
b. (7 points) Describe these data. Include any and all numerical or graphical summaries you feel are
appropriate. DO NOT simply list a series of numbers. Explain your findings using complete English
sentences (which may contain numbers, symbols, etc.).