319exam3sol - Econ 319 Fall 2008 TA Simon Kwok Exam 3...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Econ 319, Fall 2008 TA: Simon Kwok Exam 3 solutions Part 1 1. Bias of an estimator ^ & is the di/erence between the expectation of ^ & and the true characteristic & . i.e. Bias ( ^ & ) = E ( ^ & ) & & . 2. The variance of an estimator ^ & measures the variation of the estimator ^ & about its mean E ( ^ & ) . i.e. V ar ( ^ & ) = E [( ^ & & E ( ^ & )) 2 ] . 3. The signi&cance level of a test is the highest probability of rejecting the null hypothesis if it is in fact true. It is usually set by the statistician before conducting hypothesis testing. 4. The power of a test is the probability of rejecting the null hypothesis if the alternative hy- pothesis is in fact true. It is equal to one minus the probability of type II error. 5. Type I error is rejecting the null hypothesis if it is in fact true. Its probability is equal to the signi&cance level of the test. Type II error is accepting the null hypothesis if the alternative hypothesis is in fact true. Its probability is equal to one minus the power of the test. Part 2 1. (a) & X = 1 320 320 X i =1 X i , & Y = 1 206 206 X i =1 Y i . (b) E & X = 1 320 320 X i =1 E ( X i ) = 1 320 320 X i =1 ¡ X = ¡ X , so bias ( & X ) = 0 . Similarly, bias ( & Y ) = 0 . V ar ( & X ) = 1 320 2 320 X i =1 V ar ( X i ) = 1 320 2 320 X i =1 ¢ 2 X = & 2 X 320 ....
View Full Document

{[ snackBarMessage ]}

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