Chapter12 - 12.1 I nference for a Population Proportion...

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12.1 Inference for a Population Proportion 685 EXAMPLE 12.1 RISKY BEHAVIOR IN THE AGE OF AIDS How colnmon is behavior that puts people at risk of AIDS? The National AIDS Behavioral Surveys interviewed a random sample of 2673 adult heterosexuals. Of these, 170 had more than one sexual partner in the past year. That's 6.36% of the sam- p1e.l Based on these data, what can we say about the percent of all adult heterosexuals who have multiple partners? We want to estimate a single pofiulation firoportion. EXAMPLE 12.2 DOES PRESCHOOL MAKE A DIFFERENCE? Do preschool programs for poor children make a difference in later life? A study looked at 62 children who were enrolled in a Michigan preschool in the late 1960s and at a control group of 61 similar children who were not enrolled. At 27 years of age, 61% of the preschool group and 80% of the control group had required the help of a social service agency (mainly welfare) in the previous ten years.2 Is this significant evidence that preschool for poor children reduces later use of social services? We want to com- Pare two Po~ulation probortions. EXAMPLE 12.3 EXTRACURRICULARS AND GRADES What is the relationship between time spent in extracurricular activities and success in a tough course in college? North Carolina State University looked at the 123 students in an introductory chemical engineering course. Students needed a grade of C or bet- ter to advance to the next course. The passing rates were 55% for students who spent less than 2 hours per week in extracurricular activities, 75% for those who spent between 2 and 12 hours per week, and 38% for those who spent more than 12 hours per week.3 Are the differences in passing rates statistically significant? We must com- bare more than two bobulation broborh'ons. Our study of inference for proportions will follow the same pattern as these examples. Section 12.1 discusses inference for one population proportion, and Section 12.2 presents methods for comparing two proportions. Comparing more than two proportions raises new issues and requires more elaborate meth- ' ods that also apply to some other inference problems. These methods are the topic of Chapter 13. 12.1 INFERENCE FOR A POPULATION PROPORTION We are interested in the unknown proportion p of a population that has some outcome. For convenience, call the outcome we are looking for a "success." In Example 12.1, the population is adult heterosexuals, and the parameter fi is the proportion who have had more than one sexual partner in the past year. To esti- mate p, the National AIDS Behavioral Surveys used random dialing of tele- phone numbers to contact a sample of 2673 people. Of these, 170 said they
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-- 686 Chapter 12 Inference for Proportions sample proportion had multiple sexual partners. The statistic that estimates the parameter p is the sample proportion n count of successes in the sample I/ - count of observations in the sample Read the sample proportion b as "p-hat." EXERCISES In each of the following settings: (a) Describe the population and explain in words what the parameter p is.
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This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.

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Chapter12 - 12.1 I nference for a Population Proportion...

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