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Type-I and Type-II Errors and the Power of a Test for AP Statistics (page 2)

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By — McGraw-Hill Professional
Updated on Apr 25, 2014

We can reduce the probability of making a Type-II error and, at the same time, increase the power of the test in the following ways:

  • Increase the sample size.
  • Decrease the standard deviation (this is not usually under the control of the researcher).
  • Increase the significance level (α).
  • State an alternative hypothesis that is farther away from the null. In other words, do what you can to make it easier to reject H0.

example: A package delivery company claims that it is on time 90% of the time. Some of its clients aren't so sure, thinking that there are often delays in delivery beyond the time promised. The company states that it will change its delivery procedures if it are wrong in its claim. Suppose that, in fact, there are more delays than claimed by the company. Which of the following is equivalent to the power of the test?

  1. The probability that the company will not change its delivery procedures
  2. The P-value > α
  3. The probability that the clients are wrong
  4. The probability that the company will change its delivery procedures
  5. The probability that the company will fail to reject H0

solution: The power of the test is the probability of rejecting a false null hypothesis in favor of an alternative. In this case, the hypothesis that the company is on time 90% of the time is false. If we correctly reject this hypothesis, the company will change its delivery procedures. Hence, (d) is the correct answer.

Practice problems for these concepts can be found at:

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