The probability of a type II error for a hypothesis test

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The discussion focuses on calculating the probability of a type II error and the power of a hypothesis test based on a college student's driving data. The student recorded driving times and hypothesized that the mean driving time is not 2.25 hours, with the true mean being 2.5 hours. Calculations revealed a type II error probability of 0.221 and a test power of 0.779. Participants questioned the critical values' asymmetry and the significance level used in the calculations. The conversation emphasizes the importance of understanding hypothesis testing and the implications of error probabilities in statistical analysis.
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Homework Statement


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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?

Homework Equations



The equation for a t statistic

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?
 
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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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