Proportion Problems (C.I.)
STA 215: Introductory Applied Statistics
Dr. JannHuei Jinn
The following problems are related to confidence interval for population proportion.
1. Sociology: Crime Rate –
Suppose that you are a sociologist in Rock Springs,
Wyoming, and a random sample of police files showed that of 32 arrests last month, 25
were of males aged 15 to 34.
Find a 95% confidence interval for the true population
proportion of such arrests in Rock Springs. Does it capture 70%?
2. College Athletics: Graduation Rate Women athletes at the University of Colorado,
Boulder, have a longterm graduation rate of
67%
(Source: The Chronicle of Higher
Education).
Over the past several years, a random sample of 38 women athletes at the
school showed that 21 eventually graduated.
Find a 95% confidence interval for the
true population proportion. Does this interval capture 67%?
3. Highway Accidents: DUI The U.S. Department of Transportation, National Highway
Traffic Safety Administration, reported that
77%
of all fatally injured automobile
drivers were intoxicated.
A random sample of 27 records of automobile driver
fatalities in Kit Carson County, Colorado, showed that 15 involved an intoxicated
driver.
Find a 98% confidence interval for the true population proportion. Does this
interval capture 77%?
4. Highway Accidents: Airbags
Do drivers with air bags take greater risks?
Researchers
at Virginia Commonwealth University studied fatal automobile accidents between cars
in which one has an air bag and the other does not.
They found that in
73%
of all such
fatal crashes the driver of the air bag vehicle was responsible for the accident.
(Source:
See Problem 3.)
Suppose that you obtain police records of fatal automobile crashes
(involving a vehicle with an air bag and one without) near Fargo, North Dakota.
A
random sample of 41 such accidents showed that 33 were the fault of the driver of the
air bag vehicle.
Find a 98% confidence interval for the true population proportion.
Does this interval capture 73%?
5. Wildlife: Wolves The following is based on information from The Wolf in the
Southwest: The Making of an Endangered species, by David E. Brown (University of
Arizona Press).
Before 1918, the proportion of female wolves in the general
population of all southwestern wolves was about
50%
.
However, after 1918,
southwestern cattle ranchers began a widespread effort to destroy wolves.
In a recent
sample of 34 wolves, there were only 10 females.
One theory is that male wolves tend
to return sooner than females to their old territory, where their predecessors were
exterminated.
Find a 90% confidence interval for the true population proportion.
Does this interval capture 50%?
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View Full Document6. Fishing: Northern Pike: Athabasca Fishing Lodge is located on Lake Athabasca in
northern Canada.
In one of its recent brochures, the lodge advertises that
75%
of its
guests catch northern pike over 20 pounds.
Suppose that last summer 64 out of a
random sample of 83 guests did, in fact, catch northern pikes weighing over 20
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 Spring '11
 Statistics, Symposium, true population proportion

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