1. Power Problems

2. 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

3. 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

4. What is the power of the test?
H0: m = 680
Ha: m > 680
If H0 is rejected, suppose that ma is 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 = = .9529

5. What is the power of the test?
H0: m = 680
Ha: m > 680
If H0 is rejected, suppose that ma is 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 = = .7498

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

7. 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