Statistics 101: Section L
Exam 2
March 26, 2003
Name:
ID#
INSTRUCTIONS: Read the questions carefully and completely. Answer each question and show
work in the space provided. Partial credit will not be given if work is not shown. When asked to
explain, describe, or comment, do so within the context of the problem.
1. [10 pts] The following excerpt is taken from an article that appeared in the Des Moines
Register on Wednesday, September 25, 2002.
Aspirin-like drugs may cut Alzhemimer’s risk, study finds
Taking aspirin and other anti-inflammatory medications for at least two years may
reduce the risk of developing Alzheimer’s disease, according to a study.
The study, which tracked 5,092 Utah residents 65 and older, examined anti-inflammatory
medications, including ibuprofen and naproxen.
Stomach medications and other pain relievers showed no effect. But patients taking
an anti-inflammatory medication for at least two years developed Alzheimer’s at
roughly half the rate of nonusers.
The results were nearly as strong for those who used aspirin regularly . . .
One drawback is that the study involved a community of primarily Mormon residents, who tend to live more healthily and thus may not have results similar to the
general population’s, . . .
(a) [4] Is this an observational study or an experiment? Explain briefly.
(b) [3] What is the explanatory variable? What is the response variable?
(c) [3] Based on this study, should residents of Utah 65 and older take anti-inflammatory
medications to reduce their chance of getting Alzheimer’s? Explain briefly.
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2. [10 pts] Below is a list of 10 individuals who wish to attend a national convention. There is
only enough money to send two. To be fair the two will be chosen at random.
Angela
Juan
Steve
Lindsay
Mark
Jamil
Kathryn
Samantha
Melanie
Joshua
(a) [6] Use the random number table on the formula sheet (start at the left most random
number in line 120 and read left to right) to select the two. Who are they? To get full
credit it must be clear to me how you used the random number table to select the two
people.
(b) [4] If you wanted to make sure that the random selection included one woman and one
man, how would you do this?
3. [30 pts] For fall 2002, the distribution of grades in Stat 101 is given below.
Value
Grade
Probability
12
A
0.14
11
A−
0.11
10
B+
0.11
9
B
0.11
8
B−
0.12
7
C+
0.07
6
C
0.08
5
C−
0.06
4
D+
0.06
3
D
0.04
2
D−
0.02
0
F
0.08
(a) [5] What is the chance that a grade selected at random is a C or better? Below a C?
(b) [3] What is the median grade?
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(c) [5] Suppose grades are assigned a value as indicated in the first row of the table. What
is the mean value for the distribution of grades?
The standard deviation of the distribution of grades is σ = 3.515. A Stat 101 student
goes to the coordinator of Stat 101 to complain. It seems that he, and 15 of his friends,
had below a C average (an average grade value below 5).
(d) [5] Give the mean, standard deviation and describe the shape of the distribution of the
average grade value for random samples of 16 grades taken from the above grade distribution.
(e) [3] Do you need to rely on the Central Limit Theorem in order to describe the shape of
the distribution in (d)? Explain briefly.
(f) [7] What is the approximate probability that a random sample of 16 grades from the
above grade distribution would have an average grade value below 5?
(g) [2] Why is the probability in (f) not that meaningful for the student and his 15 friends?
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4. [20 pts] The following excerpt is taken from an article that appeared in the Des Moines
Register on Saturday, March 4, 2000.
Study: Meditation helps clear clogged arteries
Transcendental meditation to reduce stress helped clear clogged arteries in a group
of African-Americans, a study published Friday shows. The study used ultrasound
to measure the thickness of the carotid artery wall in 60 blacks.
The researchers . . . recruited 60 African-American men and women with high blood
pressure in the Los Angeles area.
One group was taught transcendental meditation and practiced it for 20 minutes
twice a day. A second group received health education, then spent 20 minutes,
twice a day, engaged in leisure activities such as reading or exercise.
After seven months, the meditating group had a mean reduction in artery wall
thickness of 0.098 millimeters. The wall thickness in the control group increased
by 0.054 millimeters.
(a) [4] Is this an observational study or an experiment? Explain briefly.
(b) [3] What is the explanatory variable? What is the response variable?
(c) [5] What important information about a well designed study is not mentioned?
(d) [5] What is a blind study? Is this a blind study? Explain briefly?
(e) [3] Someone reading this article might conclude that everyone should practice transcendental meditation to reduce artery wall thickness. Based on the information in the
article, is this a valid conclusion? Explain briefly.
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5. [10 pts] Random samples are taken from a population whose measurements have a skewed
distribution like the one pictured below.
The sampling distributions of the sample mean for different size samples (n=5, 10, 25, 100)
are given below.
(a) [6] Match the correct sample size to the sampling distribution. Explain your reasoning
briefly.
(b) [4] Is this an example of the Central Limit Theorem? Explain briefly?
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6. [15 pts] At one particular apple orchard apples are randomly placed in bags of 25 and sold
for $5 a bag. Because apples vary in weight, each bag of 25 apples is weighed and the average
weight of apples in the bag is printed on the price tag. The distribution of the average weight
of apples is approximately normal with center at 4.2 ounces and spread of 0.07 ounces.
(a) [7] What is the chance that a bag, with 25 apples, will have an average weight greater
than 4 ounces?
(b) [8] What can you say about the distribution of individual apple weights? Specifically;
• [2] What is the center (population mean apple weight)?
• [3] What is the spread (population standard deviation of apple weights)?
• [3] What is the shape of the distribution of apple weights?
7. [5 pts] What is replication in an experiment and why is it important?
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