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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
Slide 3
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
!
Slide 4
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