{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ps03 - Statistics 403 Problem Set 3 Due in lab on Friday...

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

View Full Document Right Arrow Icon
Statistics 403 Problem Set 3 Due in lab on Friday, October 1st 1. Suppose we are interested in estimating a quantity μ , and we can obtain independent measurements X i with EX i = μ . We intend to use ¯ X to estimate μ , and we wish to have the probability of the estimation error being greater than 0 . 1 units be equal to 0.1. What sample size is required if the standard deviation σ = SD( X i ) is (i) σ = 0 . 5 or (ii) σ = 0 . 2? You can treat ¯ X as being normally distributed. Solution: For this problem, I was thinking of the error as being the absolute difference between the estimate and the true value, | ¯ X - μ | . But if you use the signed error ¯ X - μ , that’s OK this time. The following calculation gives the probability of the absolute error being greater than 0 . 1 units: P ( | ¯ X - μ | > 0 . 1) = 2 P ( ¯ X - μ > 0 . 1) = 2 P ( n ¯ X - μ σ > 0 . 1 n/σ ) = 2 P ( Z > 0 . 1 n/σ ) We want an error larger than 0.1 to occur only 0.1 fraction of the time, so we set 2 P ( Z > 0 . 1 n/σ ) = 0 . 1 , or P ( Z > 0 . 1 n/σ ) = 0 . 05 .
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the 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