STAT100B_HW2S - STAT 100B Homework 2 Solutions Denise Tsai...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 100B: Homework 2 Solutions Denise Tsai January 31, 2011 1. Suppose we flip a coin 100 times independently and we get 55 heads. (a) Test H 0 : p = 1 / 2 vs H 1 : p > 1 / 2, and calculate the p-value. Solution: Z = ˆ p - p 0 q p 0 (1 - p 0 ) n = 55 100 - 0 . 5 0 . 5(1 - 0 . 5) 100 = 1 The p-value: P ( Z > 1) = 1 - P ( Z 1) = 1 = 0 . 8413 = 0 . 1587 We do not reject the null hypothesis. Therefore, there is strong evidence to claim that the coin is fair. (b) Suppose the decision rule is to reject H 0 if ˆ p > . 6. What is the probability of type I error? If the true value of
Image of page 1
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