Power Problems.

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Presentation transcript:

Power Problems

What is the probability of committing a Type I error? A researcher selects a random sample of size 49 from a population with standard deviation s = 35 in order to test at the 1% significance level the hypothesis: H0: m = 680 Ha: m > 680 What is the probability of committing a Type I error? a = .01

H0: m = 680 Ha: m > 680 For what values of the sample mean would you reject the null hypothesis? Invnorm(.99,680,5) =691.63

What is the power of the test? H0: m = 680 Ha: m > 680 If H0 is rejected, suppose that ma is 700. What is the probability of committing a Type II error? What is the power of the test? Normalcdf(-10^99,691.63,700,5) =.0471 Power = 1 - .0471 = .9529

What is the power of the test? H0: m = 680 Ha: m > 680 If H0 is rejected, suppose that ma is 695. What is the probability of committing a Type II error? What is the power of the test? Normalcdf(-10^99,691.63,695,5) =.2502 Power = 1 - .2502 = .7498

Fail to Reject H0 Reject H0 a ma m0 Power = 1 - b b

Facts: The researcher is free to determine the value of a. The experimenter cannot control b, since it is dependent on the alternate value. The ideal situation is to have a as small as possible and power close to 1. (Power > .8) As a increases, power increases. (But also the chance of a type I error has increased!) Best way to increase power, without increasing a, is to increase the sample size