Power of a test. power The power of a test (against a specific alternative value) Is In practice, we carry out the test in hope of showing that the null.

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Presentation transcript:

Power of a test

power The power of a test (against a specific alternative value) Is In practice, we carry out the test in hope of showing that the null hypothesis is false, so

H 0 True H 0 False Reject Fail to reject

A researcher selects a random sample of size 49 from a population with standard deviation  = 35 in order to test at the 1% significance level the hypothesis: H 0 :  = 680 H a :  > 680 What is the probability of committing a Type I error?

H 0 :  = 680 H a :  > 680 For what values of the sample mean would you reject the null hypothesis?

H 0 :  = 680 H a :  > 680 If H 0 is rejected, suppose that  a is 700. What is the probability of committing a Type II error? What is the power of the test?

H 0 :  = 680 H a :  > 680 If H 0 is rejected, suppose that  a is 695. What is the probability of committing a Type II error? What is the power of the test?

00  aa Fail to Reject H 0 Reject H 0

What happens to , , & power when the sample size is increased? Reject H 0 Fail to Reject H 0 00  aa 

Facts:

Bottles of a popular cola are suppose to contain 300 ml of cola. A consumer group believes the company is under-filling the bottles. (Assume  = 50 with n = 30) Find the power of this test against the alternative  = 296 ml.