Chapter 9.1-9.2 - Math3200 Intermediate Probability and Statistics Prof Nan Lin Department of Mathematics Washington University Outline Inferences for

Chapter 9.1-9.2 - Math3200 Intermediate Probability and...

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Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University

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Outline Inferences for proportions One-sample Two-sample Nan Lin, Washington University 2
One-sample inference for proportion (large sample) Data: a random sample ? 1 , … , ? 𝑛 from Bernoulli(p) Point estimate of the probability parameter ? ? = ? ? = ? 𝑖 𝑛 𝑖=1 ? Sampling distribution For large sample, ?? ≥ 10 and ?(1 − ? ) ≥ 10 , based on the CLT ? ∼ 𝑁 ?, 𝑝 1−𝑝 𝑛 Therefore, 𝑃 −? 𝛼 2 𝑝 −𝑝 𝑝 1−𝑝 𝑛 ≤ ? 𝛼 2 = 1 − 𝛼 After some rearrangement and replacing ? by ? in the standard deviation, we have the 100 1 − 𝛼 % confidence interval of ? ? − ? 𝛼 2 ? 1 − ? ? ≤ ? ≤ ? + ? 𝛼 2 ? 1 − ? ? Nan Lin, Washington University 3

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100 1 − 𝛼 % confidence interval of ? Two-sided confidence interval ? − ? 𝛼 2 ? 1 − ? ? ≤ ? ≤ ? + ? 𝛼 2 ? 1 − ? ? Lower one-sided ? ≥ ? − ? 𝛼 ? 1 − ? ? Upper one-sided ? ≤ ? + ?
• Spring '08
• SAWYER
• Statistics, Probability, Statistical hypothesis testing, Washington University, Nan Lin, Prof. Nan Lin

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