sample207_1 - Sample problems 2 1 Consider the following...

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

View Full Document Right Arrow Icon
Sample problems 2 1. Consider the following random sample: - 2 . 5, 0 . 3, 1 . 5, - 1 . 2, - 1 . 4, - 2 . 0, - 1 . 7, 1 . 5, 1 . 2, 2 . 0, - 0 . 5, 1 . 1. Test the hypothesis that this comes from a t-distribution with 1 degree of freedom. Use α = 0 . 05 Solution: Since n = 12, we should use no more than 4 bins. Let’s set up the bins in such a way that the expected frequency in each bin is equal to 3. Since t 0 . 25 , 1 = 1 . 000, the bins should be x < - 1, - 1 < x < 0, 0 < x < 1, and x > 1, respectively. So the observed frequencies become: O 1 = 5, O 2 = 1, O 3 = 1 and O 4 = 5. The value of the test statistic is χ 2 0 = 1 3 2 2 + 2 2 + 2 2 + 2 2 · = 5 . 33 . Since χ 2 0 . 05 ,k - p - 1 = χ 2 0 . 05 , 4 - 0 - 1 = χ 2 0 . 05 , 3 = 7 . 81, we can’t reject the null hypothesis and conclude that it is plausible. 2. Out of 70 Lehigh students 50 like Heineken more than Beck’s, and out of 60 Lafayette students, 35 prefer Heineken to Beck’s. Is it reasonable to believe that the beer preference is independent of the place of study? Solution: Let’s compute the expected frequencies.
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