Inference as Decision Section 10.4.

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Presentation transcript:

Inference as Decision Section 10.4

Type I error If we reject Ho (accept Ha) when in fact Ho is true Type II error If we accept Ho (reject Ha) when in fact Ha is true

Truth about the population Decision based on sample H0 True Ha True Type I error Correct Decision Type II error Reject H0 Accept H0

Significance and Type I error The significance level  of any fixed level test is the probability of a Type I error That is ,  is the probability that the test will reject the null hypothesis Ho when Ho is in fact true

Power The probability that a fixed level  significance test will reject Ho when a particular alternative value of the parameter is true is called the power of the test against that alternative

The power of a test against any alternative is 1 minus the probability of a Type II error for that alternative Calculations of power are essentially the same as calculations of the probability of Type II error

P-values describe what would happen supposing that the null hypothesis is true Power describes what would happen supposing a particular alternative is true

Calculating Power State Ho, Ha, the particular alternative we want to detect, and the significance level  Find the values of x bar that will lead us to reject Ho Calculate the probability of observing these values of x bar when the alternative is true

Four Ways to Increase Power Consider a particular alternative that if farther away from o Increase the sample size Decrease 

Practice Problems Section 10.4 Chapter Review pg. 605 #10.74-10.77