Download E1-06 - University of Minnesota

PubH 6450
Exam 1 (10/5/06)
NAME:_________________________
Lab Session (Day and Time)_________________________
Directions: This is an open-book, open-notes exam; however, sharing of books, notes,
homework papers, calculators, or verbal comments is not permitted. You may use a
calculator of your choosing, but laptop computers are not permitted. For true/false
questions, please clearly indicate your answer. For short answer problems, please show
all relevant work necessary to arrive at a solution, as partial credit will be awarded. You
will have from 1:30pm to 3:15pm to complete this exam, so do not spend too much time
on any one problem. Good Luck!!
1. Below are separate stemplots for the ages of men reporting for a particular colorectal
cancer screening procedure at two clinics, one in Minneapolis and the other in St. Paul:
Minneapolis
St. Paul
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5
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7
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3
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0
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4
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3 9
4 7 8
8 8
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2 6 7 8 8
3 5 5 5
3 3 7
a.
Find the median ages in both clinics.
b.
Determine whether each of the following statements is true or false:
(i)
The Minneapolis plot is bimodal.
(ii)
The lowest age observed in either clinic is 29.
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c. Find the five-number summary (min, Q1, median, Q3, max) for the combined data
from both clinics.
d. Use the 1.5 IQR criterion to find the upper and lower outlier cutoffs for this
combined dataset. List any outliers that are identified by these cutoffs.
2. A histogram of University of Minnesota faculty salaries is strongly skewed to the
right, with many modest salaries but a few very large ones (corresponding mostly
to surgeons and football coaches). Which measure of center, the mean or the
median, is larger?
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3. A company produces packets of soap powder labeled “Giant Size 32 oz.” The actual
weight of soap powder in such a box has a normal distribution with a mean of 33 oz. and
a standard deviation of 0.7 oz.
a.
The federal government considers a box of soap to be underweight if it weighs less than
32 oz. What proportion of boxes is underweight?
b.
What proportion of boxes weighs between 32.65 and 33.7 oz?
c.
The company loses money on the top (heaviest) 5% of boxes, which it wishes to label as
overweight. How heavy does a box have to be in order to receive this label?
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4. Suppose a bag contains candy of six different colors, for which the proportions of each
color are as follows:
Color
Proportion
Brown
0.3
Red
0.3
Yellow
?
Green
0.1
Orange
0.1
Blue
0.1
a.
Suppose we draw one candy from the bag at random. What is the probability of
drawing a yellow candy?
c.
If you independently select two candies from the bag, with replacement, what is the
probability that both are the same color?
5. The weight W of a medium-size tomato selected at random from a bin at the local
supermarket is a random variable with mean  = 10 oz. and standard deviation  = 2 oz.
a.
Suppose we pick two tomatoes at random from the bin. Let the random variable
S = the sum (in ounces) of the weights of the two tomatoes selected. What is the mean
and standard deviation of the random variable S?
b.
Let the random variable Z = the weight of a randomly selected tomato in pounds, where
1 pound = 16 oz. What is the standard deviation of the random variable Z?
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6. Suppose that out of every 10,000 people age 60 and over, 800 will have colorectal
cancer. Of these, 600 will have a positive hemoccult test. Out of the remaining
9200 people without colorectal cancer, 300 will still test positive. How many of
those who test positive actually have colorectal cancer?
7. An investigator samples 20 households having two parents and a newborn child,
in which both parents have chronic bronchitis. She notices that in 3 of these
households, the child also develops chronic bronchitis in the first year of life. The
national incidence rate of bronchitis among all children is 5% in the first year of
life. Let X be a random variable representing the number of children in the
investigator’s sample who will develop bronchitis in the first year of life.
a.
What is the appropriate distribution for X assuming the children in the investigator’s
study are typical of children nationwide?
b.
Using this distribution, what is the expected number of children in the sample who will
develop bronchitis?
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8. Compute the probability that the mean birth-weight from a sample of 10 infants
will fall between 98 and 120 ounces if the mean birth-weight for the population is
known to be 112 ounces with a standard deviation of 20.6 ounces.
9. A special study is conducted to test the hypothesis that people with glaucoma
have higher blood pressure than average. In the study, the 200 people with
glaucoma recruited have a mean systolic blood pressure of 140 mmHg. Assume
the population distribution of systolic blood pressure is normally distributed and
has a standard deviation of = 25 mmHg.
a. Construct a 95% confidence interval for the true mean systolic blood
pressure among people with glaucoma.
b. What is the margin of error, m, for your confidence interval? What
sample size would be needed to deliver a margin of error of just m/3 ?
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