{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

5102-Lecture-11

# 5102-Lecture-11 - Lecture 11 Stat 5102-004 11 February 2011...

This preview shows pages 1–5. Sign up to view the full content.

Lecture 11 Stat 5102-004 11 February 2011

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Confidence Regions Let B be a set whose elements are subsets of the parameter space ϑ . B ∈ B = B ϑ The region estimator ˆ B γ : Y → B is a level γ confidence region if Pr( θ ˆ B γ ) = γ for all θ ϑ . The confidence region is approximate if Pr( θ ˆ B γ ) γ for all θ ϑ . STAT 5102 (Theory of Statistics) Lecture 11 1 / 9
Normal Mean, Variance Known Let Y 1 , . . . , Y n iid N( μ, σ 2 ) with σ 2 known. Pr ¯ Y - σ n z ( γ ) μ ¯ Y + σ n z ( γ ) = γ point estimate ± standard error × critical value ˆ B γ ( y ) = ¯ y + - σ n z ( γ ) , σ n z ( γ ) z (0 . 90) = 1 . 645 z (0 . 95) = 1 . 96 z (0 . 99) = 2 . 576 Pr( μ ˆ B γ ) = γ for all μ STAT 5102 (Theory of Statistics) Lecture 11 2 / 9

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Normal Mean, Variance Known, γ = 0 . 90 ● ● ●● ●● ●● ●● ●● ●● ● ● ● ●● ●●● ●● ●●● ● ● ●● ●● ●● ●● ● ● ●● ● ● ● ● ●● ●● μ - 2 σ n μ μ + 2 σ n μ - 2 σ n μ μ + 2 σ n STAT 5102 (Theory of Statistics)
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern