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...

This preview shows page 1 - 5 out of 14 pages.

Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University
Image of page 1

Subscribe to view the full document.

Outline Inferences for proportions One-sample Two-sample Nan Lin, Washington University 2
Image of page 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
Image of page 3

Subscribe to view the full document.

100 1 − 𝛼 % confidence interval of ? Two-sided confidence interval ? − ? 𝛼 2 ? 1 − ? ? ≤ ? ≤ ? + ? 𝛼 2 ? 1 − ? ? Lower one-sided ? ≥ ? − ? 𝛼 ? 1 − ? ? Upper one-sided ? ≤ ? + ?
Image of page 4
Image of page 5
  • Spring '08
  • SAWYER
  • Statistics, Probability, Statistical hypothesis testing, Washington University, Nan Lin, Prof. Nan Lin

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes