Slide 1

Power of a Test Notes: P 183 and on your own paper

Slide 2

power p. 183 The power of a test (against a specific alternative value) Is the probability that the test will correctly reject the null hypothesis when the alternative is true In practice, we carry out the test in hope of showing that the null hypothesis is false, so high power is important

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H 0 True H 0 False Reject Fail to reject Type I Correct Type II Power Suppose H 0 is true what if we decide to fail to reject it? Suppose H 0 is false what if we decide to reject it? Suppose H 0 is true what if we decide to reject it? Suppose H 0 is false what if we decide to fail to reject it? We correctly reject a false H 0 !

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p. 178 A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. In a test, vaccinated people were exposed to the flu. Is this claim too high? Identify the following decisions: We decide the true proportion of vaccinated people who do not get the flu is less than 70% when in fact it really is less. Correct decision!

Slide 5

A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. In a test, vaccinated people were exposed to the flu. Is this claim too high? Identify the following decisions: We decide the true proportion of vaccinated people who do not get the flu is not less than 70% when in fact it really is less. Type II error

Slide 6

A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. A random sample of 100 people are vaccinated and then exposed to the flu. Is this claim too high? Use =.05. What are the hypotheses? H 0 : p =.7 H a : p