ECO 252
Summer 2001
Formulas
Second Exam
Dr. Andrews
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 (1   )
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Name________________________
Introductory information: (this is not a question)
On the industrial riverbank of Chester, a block-long warehouse roared with explosions and spewed noxious
smoke. Fireballs somersaulted through its caving roof. Inside and out, stacked rows of rusting drums roasted
in the heat. They swelled up fat, then blew and hurtled like 55-gallon missiles, spraying foul liquids.
Staggering from the warehouse, retching and gasping for air, came Vincent "Moose" McLaughlin, 38, a tall,
rugged fire captain revered by the men he now feared were lost. His throat was scorched raw, his eyes pink
and sore, his face and neck flushed with an itchy red rash. He coughed his lungs clear, vomited in the mud,
and charged back inside, feeling along a hose line for his cut-off platoon. He made four or five plunges, all
without breathing gear, before he found them, snatching one young apprentice by the coat from an iridescent
pool of sludge. As darkness gathered on Feb. 2, 1978, similar horrors played across the seared grounds of
Eastern Rubber Reclaiming Inc., an old rubber-shredding plant beneath the Commodore Barry Bridge.
More than 200 firefighters, police and paramedics had answered the alarm, assuming a tire fire had erupted.
Instead, they waded unwarned into one of the worst illegal chemical dumps in the nation – a witches' brew
so poisonous that the federal Superfund was born, in part, from it. The inferno at 1 Flower Street also was
the opening scene in a private tragedy still unfolding today. Disease is decimating the ranks of those who
fought the blaze, according to an Inquirer investigation that traced nearly all who had been there.
The Inquirer, which tracked down 207 people who had been to the blaze, provided the researchers with
detailed data on 199, including age, race, date of diagnosis and, if available, smoking history. Information
also was assembled on the amount of time each person spent at the scene, his proximity to the fire, and skin
contact with chemicals. The epidemiologists eliminated 18 individuals for whom some information was
lacking.
The analysis found elevated rates of both lung cancer and melanoma.
For each problem state the null and alternative hypotheses in symbols, show all your work, and
explain your results. (The conclusion you reach may differ for different tests, i.e., you may reject in
one test and fail to reject in another.)
1. There were four cases of melanoma among the 181 people studied. The number expected in the general
population .36 percent (.0036). The incidence of the disease among the group, therefore, was roughly six
times higher. "The elevated risk of melanoma is striking," the epidemiologists wrote. "The occurrence of
the four melanomas is somewhat unusual." Evaluate the epidemiologist’s statement using a hypothesis test.
Ho: π ≤ .0036 (Melanoma rates are no worse than in the general population
Ho: π > .0036 (Melanoma rates are worse than in the general population)
CV Reject Ho
1.96
TS= .022 -
p 
 (1   )
n

.022  .0036
.0036(1  .0036)
181

4.08
.022  .0036 .0184
 4.08
.0045
1.98
In this case we can be 99.99 percent sure that the melanoma rate is higher than the general population.
2. On average across the nation, firefighters miss time due to illness an average of 9 days per year with a
standard deviation of 3 days. Personnel records for the 27 firefighters involved in the blaze who still
work for the city showed that those involved missed an average of 11.2 days last year. Does it appear
that these firefighters are missing more days due to illness? Explain your answer.
Ho: μ ≤ 9 (illness rates are no worse than in the general population
Ho: μ > 9 (Melanoma rates are worse than in the general population)
CV Reject Ho
1.96
x
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
n
3.81
11.2  9 2.2

 3.81
3
.57
27
In this case we can be 99.99 percent sure that the ilness rate is higher than the general population. However,
the sample size is too small, and since sick days are discrete, the distribution of sick days cannot reasonably
be assumed to be normal.
3. Eastern Rubber Reclaiming Inc., asserts in its defense that the fire fighters are several years older than
the general population, and that is why disease rates are so high. The average age of a sample of 82
firefighters was 35.3 years with a standard deviation of 4 years. The average age of the general population
is only 30, and the company thinks that the firefighters were at 34 on average. Evaluate the company’s
statement using a hypothesis test.
Ho: μ ≤ 34
Ho: μ > 34 firefighters are at least 34
CV Reject Ho
1.664
x
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n
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3.81
35.3  34 1.3

 2.94
4
.44
82
In this case we can be 99.8 percent sure that the average age of all firefighters was over 34.