The probability of a type II error for a hypothesis test

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SUMMARY

The discussion focuses on calculating the probability of a type II error for a hypothesis test involving a college student's driving time data. The student sampled 15 rest stops and hypothesized that the true mean driving time is not 2.25 hours, with the actual mean being 2.5 hours. The calculated probability of a type II error is 0.221, and the power of the test is 0.779. The critical values for the t statistic were determined to be t < -3.463 or t > 0.7991, indicating an unequal spacing around zero due to the significance level used.

PREREQUISITES
  • Understanding of hypothesis testing concepts
  • Familiarity with t statistics and critical values
  • Knowledge of type I and type II errors
  • Ability to perform calculations using statistical software or calculators
NEXT STEPS
  • Learn about the calculation of power in hypothesis testing
  • Study the implications of type I and type II errors in statistical analysis
  • Explore the use of statistical software for hypothesis testing
  • Investigate the significance levels and their impact on critical values
USEFUL FOR

Students in statistics courses, researchers conducting hypothesis tests, and data analysts looking to understand error probabilities in their analyses.

Mr Davis 97
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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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