Download 1 PubH 6414 NAME: Practice Exam 2 1. Cervical cancer patients

PubH 6414
Practice Exam 2
NAME:______________________
1. Cervical cancer patients have high chances of long-term survival when the cancer
is detected early. The Pap smear is a diagnostic screening tool for cervical cancer.
Denote presence of cervical cancer as D+ and absence of cervical cancer as D-.
Denote a positive Pap smear as T+ and a negative Pap smear as T-. Suppose:
Pr(T+ | D-)=0.1864
Pr(T- | D+) = 0.1625
(false positive rate)
(false negative rate)
a. What is Pr(T+ | D+)? (sensitivity)
b. What is Pr(T- | D-)? (specificity)
c. Suppose Pr(D+)=0.000083 (i.e., there are 8.3 cervical cancer cases per
100,000 women). What is Pr(D+ | T+)? (positive predictive value)
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2. Suppose the amount of money spend on health care for an average American
household for one year is normally distributed with an mean µ= $3000 and a
standard deviation of σ = $450.
a. Suppose your household spends $4,300 this year on health care, what is
the Z score for your household?
b. Suppose your neighbors had a Z score of -1.4 for this year. How much did
they spend of health care this year?
c. What probability American households spend less than $2550 a year on
health care?
d. An American household would have to spend what amount on healthcare
to be in the top 2.5% of spenders?
e. Suppose we repeatedly take samples of size 49. What is the sampling
distribution of the sample mean X ? (Give the name of the distribution
and the values of its mean and standard deviation.)
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3.
A questionnaire was given to the 212 attendants of the 1988 annual meeting for
the New Jersey Society for Medical Technology. (Attendants of this meeting are
laboratory workers who handle serum samples.) One of the questions was, “I feel
my employer offers adequate counseling in the event of an accident with HIV
positive samples.” 41 responses were “Yes” and 171 responses were “No.”
Suppose the population of interest is all such laboratory workers in the US, and
we know for this population that the proportion of ‘yes’ responses is 0.26.
a. Let X = number of ‘yes’ responses. Does X follow a Binomial
distribution? Justify your answer.
b. If so, which Binomial distribution does it follow? Give the values for any
necessary parameters.
c. What is the expected number of ‘yes’ responses in this sample of 212?
What is the standard deviation in number of ‘yes’ responses?
d. Again suppose the population of interest is all such laboratory workers in
the US, and we know for this population that the proportion of ‘yes’
responses is 0.26. Now using the Central Limit Theorem, write down the
sampling distribution for the number of ‘yes’ responses.
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4. In response to the increasing weight of airline passengers, the Federal Aviation
Administration in 2007 started taking random samples of the weights of
passengers to try to estimate the true mean weight. Suppose a sample of 121
passengers yields an average weight of 190 pounds with a standard deviation of
35 pounds.
a. [Note: P( -1.645 <t120 < 1.645) = 0.90. Construct a 90% confidence
interval for µ.
b. If instead of a sample of 121, the airlines took a sample of 1000, would the
90% confidence interval be wider or narrower (assume s =35 pounds for
both samples)?
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5.
Suppose the weights in pounds for the population of U.S. men aged 20-29 years
is normally distributed with mean µ = 178 pounds and standard deviation σ = 37
pounds (Source: table 244, Statistical Abstract of the US: 1999).
a. Brian is a 22 year old American man. He weighs 260 pounds. How many
standard deviations above the mean is his weight?
b. Frank is a 28 year old American man. His weight is 1.2 standard
deviations below the mean. What does he weigh in pounds?
c. What percent of U.S. men ages 20-29 years weight less than 178 pounds?
d. Suppose we take a simple random sample of 16 men from this population.
What is the sampling distribution of the mean? List the shape and any
parameter values.
e. What is the probability that the mean from a random sample of 16 men
from this population is less than 159.5 pounds?
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6. In a 1995 study in Los Angeles, investigators examined 752 randomly selected
medical records for 2-year old children. They found that 202 children have had
all of their vaccinations and 550 children had missed some immunizations.
(Source: Am J of Public Health, 1995, 85: 850-853).
a. Suppose that overall in the U.S. population it is known that 30% of
children have had all of their vaccinations. What is the expected number
of children who have had all of their vaccinations in a sample of size 752?
b. What is the standard deviation of the number of children who have had all
of their vaccinations in a sample of size 752?
c. Using the Central Limit Theorem (Normal Approximation), write down
the sampling distribution for the number of children who have had all of
their vaccinations in a sample of size 752? List the shape and any
parameter values.
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7. In addition to the vaccination records, (question 4) the investigators found in their
sample from Los Angeles, that the kids who have had their vaccinations (n = 202
) visited the clinic on average 8.2 times a year with a standard deviation of s = 3.8.
a. Construct a 95% confidence interval for µ (the population average number
of clinic visits a year for kids who have had their vaccinations in Los
Angeles). Note: P(-1.972 < t 201< 1.972 ) = .95
b. For this sample, is the 99% confidence interval narrower or wider than the
95% confidence interval?
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