Chap11 - Chapter 11 Hypothesis Testing 1 I Inference in...

Info icon This preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Chapter 11 Hypothesis Testing
Image of page 1

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

View Full Document Right Arrow Icon
2 Correct acceptance of H 0 pr(I= H 0 | T=H 0 ) = (1 – α ) Type I Error pr(I= H 1 | T=H 0 ) = α [aka size ] Type II Error pr(I= H 0 | T=H 1 ) = β Correct acceptance of H 1 pr(I= H 1 | T=H 1 ) = (1 – β ) [aka power ] I : Inference in favor of: H 1 : Alternative Hypothesis H 0 : Null Hypothesis H 0 : Null Hypothesis T : The Truth of the matter: H 1 : Alternative Hypothesis
Image of page 2
3 Before diving into the “nuts and bolts” details, let’s consider the “big picture” of statistical testing Example from p. 394
Image of page 3

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

View Full Document Right Arrow Icon
4 Components of a statistical test: Background assumptions Hypotheses Test statistic Determine the critical bound(s) Interpret/Report the results.
Image of page 4
5 1. For the results of a test for the mean of a population to have any meaning, the drawings from the sample must be: Independent Identically distributed 2. The underlying population must be approximately normal This assumption is frequently violated But when we use and a fairly large n (e.g., n ≥ 20), the CLT usually makes this true. Background Assumptions X
Image of page 5

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

View Full Document Right Arrow Icon
6 We usually form only two hypotheses The null hypothesis: H 0 The alternative hypothesis: H 1 In this class, H 0 is always a very specific hypothesis about the precise value of some parameter E.g., we might use: H 0 : μ = 120 Hypotheses
Image of page 6
7 Test Statistic For a test of the mean, we will use , often in its standardized form as a t- statistic comes from an unbiased and consistent point estimator x n s x s x h x h 0 0 μ μ - = - x
Image of page 7

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

View Full Document Right Arrow Icon
8 Accept H 0 Accept H 1 Critical Bound:
Image of page 8
9 A critical bound acts as a threshold: If our data results in a number less than the critical bound, we accept the hypothesis with the smaller mean (in this case, H 0 ) If our data results in a number greater than or equal to the critical bound, we accept the hypothesis with the larger mean (in this case, H 1 ) Determining a Critical Bound
Image of page 9

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

View Full Document Right Arrow Icon
10 Determining a Critical Bound We will adopt the common practice of using α to determine our critical boundary α = pr(decide in favor of H 1 | H 0 is true) How much of a risk are we willing to take of incorrectly inferring that H 1 is true when H 0 actually is? No matter what we do, we will have to take some chance (i.e., α > 0)
Image of page 10
11 Determining a Critical Bound A common choice of α is .05. This choice means that we will set our critical bound so that only 5% of the distribution of H 0 is beyond it: This can be determined using quantiles: @qnorm(.95) = 1.64 @qtdist(.95, 19) = 1.73 @qtdist(.95, @obs(x)-1) = 1.73 95 . ) 64 . 1 ( = Φ df = n – 1
Image of page 11

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

View Full Document Right Arrow Icon
12 Only α of H 0 ’s distribution (1 – α ) of H 0 ’s distribution μ H0 Accept H 0 Accept H 1 Critical Bound: 1.64, if: 2200 α = .05 n= 1, and H 0 = N(0, 1)
Image of page 12
13 Determining a Critical Bound Intuitively, we want to find the number b such that: Similar to confidence intervals, we use α to determine a quantile q which then determines the boundary b 05 . | 0 0 = - H q S X pr X H μ ( 29 05 . | 0 = H b X pr
Image of page 13

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

View Full Document Right Arrow Icon
14 Determining a Critical Bound As with confidence intervals, it is easy to transform our standardization into an
Image of page 14
Image of page 15
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