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8_1_Handout - 8.1 Inference for a Single Proportion...

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8.1 Inference for a Single Proportion Large-sample confidence interval for a population proportion Choose an SRS of size n from a large population with unknown proportion p of successes. The sample proportion is: p ˆ = n X where X is the number of successes. The standard error of p ˆ is: p SE ˆ = n p p ) ˆ 1 ( ˆ - and the margin of error for confidence level C is: m =( z *)( p SE ˆ ) where z * is the value for the standard normal density curve with area C between – z * and z *. A approximate level C confidence interval for p is p ˆ ± m Use this interval for 90%, 95%, or 99% confidence when the number of successes and the number of failures are both at least 15.
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EX 1) A survey of 17,096 students in US four-year colleges collected information on drinking behavior. The researchers defined “frequent binge drinking” as having five or more drinks in a row three or more times in the past two weeks. According to this definition, 3314 students were classified as frequent binge drinkers. Compute the 95%
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8_1_Handout - 8.1 Inference for a Single Proportion...

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