215 proportion problems(CI), Summer 2008

# 215 proportion problems(CI), Summer 2008 - Proportion...

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Proportion Problems (C.I.) STA 215: Introductory Applied Statistics Dr. Jann-Huei 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 long-term 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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6. 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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215 proportion problems(CI), Summer 2008 - Proportion...

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