Statistics 101
Exam 2
March 13, 2002
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] 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) [5] Use the random number table on your 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) [5] If you wanted to make sure that the random selection included one woman and one
man, how would you do this?
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2. [17 pts] The weights of small bags of almond M&Ms are assumed to be normally distributed
with mean µ = 56.8 grams and standard deviation σ = 1.8 grams.
(a) [5] What proportion of small bags of almond M&Ms weigh less than 54 grams?
(b) [6] Overfilling bags costs the company money. What is the maximum weight such that
only 1.3% of small bags of almond M&Ms will weigh more?
(c) [6] By sorting the almonds, one can get greater consistency (less variability). What
would the standard deviation be such that 10% of small bags of almond M&Ms weigh
more than 58.0 grams?
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3. [17 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) [3] Is this an observational study or an experiment? Explain briefly.
(b) [2] What is the explanatory variable? What is the response variable?
(c) [5] What important information about a well designed study is not mentioned?
(d) [4] 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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4. [18 pts] The Iowa State Daily on Friday, September 24, 1999 ran an article stating that
“Students who belong to sororities have a higher average grade point than other Iowa State
students.” The article went on to indicate that sorority women maintained an average grade
point of 2.94, which was considerably higher than the all university mean. The distribution
of grade points for all students at ISU is approximately normal with center µ = 2.84 and
spread σ = 0.38.
(a) [6] Suppose we have 64 women selected at random from all students at ISU. What is
the chance that the average grade point for these 64 women is greater than or equal to
2.94?
(b) [2] Do you think that the 64 women in a sorority could be a random sample from all
ISU students? Explain briefly.
(c) [6] Women have traditionally earned higher grade points than men. At ISU the distribution of women’s grade points has a center µ = 2.92 and a spread σ = 0.36. What is
the chance that the average grade point for a random sample of 64 women selected from
all women at ISU is greater than or equal to 2.94?
(d) [4] Do you need the Central Limit Theorem to justify your answer to either part (a) or
(c)? Explain briefly.
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5. [13 pts] The following is excerpted from an article written by Paul Recer, Associated Press,
that appeared in the February 6, 2002 Des Moines Register.
Study: Tanning raises cancer risk.
In a study in today’s Journal of the National Cancer Institute, researchers
found that people who used tanning devices were 1.5 to 2.5 times more
likely to have common kinds of skin cancer than were people who did not
use the devices.
Researchers interviewed 896 patients with basal cell or squamous cell skin
cancer and 540 people who did not have either cancer.
Among the skin cancer patients, 190 reported using tanning devices at some
time. Of those without skin cancer, only 75 had used tanning devices.
(a) [3] Is this an observational study or an experiment? Explain briefly.
(b) [2] What are the response and the explanatory variables?
Below is a tabulation of the 1436 people in the study.
skin
cancer
no skin
cancer
190
75
265
706
465
1171
896
540
1436
used
tanning
devices
didn’t use
tanning
devices
(c) [3] Looking only at those who used tanning devices, what is the chance (empirical probability) of having skin cancer?
(d) [2] Is the chance in (c) greater than or smaller than the chance of having skin cancer for
all 1436 people?
(e) [3] Does this study establish the use of tanning devices as a cause of skin cancer? Explain briefly.
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