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The probability of a type II error for a hypothesis test

  1. Apr 19, 2015 #1
    1. The problem statement, all variables and given/known data

    1. After a long road trip during summer break, a college student wants to estimate how long she drove between rest stops. She takes a random sample of 15 stops and records this data in hours: 1.5, 2.6, 1.75, 3.5, 2.25, 3.75, 1.8, 2.9, 3.2, 3.15, 1.5, 2, 3, 2.75, and 2.2. She thinks that the real mean is not 2.25 hours. Given that the true mean is 2.5 hours, what is the probability that she will make a type II error? What is the power of the test?


    2. Relevant equations

    The equation for a t statistic

    3. The attempt at a solution

    With my calculator, I found that we reject the null hypothesis when t < -3.463 or when t > .7991. I found P(type II error) = .221, and the power of the test to be .779. Is this correct?
     
  2. jcsd
  3. Apr 20, 2015 #2

    statdad

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    Homework Helper

    Why are your critical values not equally spaced either side of 0? What significance level were you using? What work did you do to get the power?
     
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