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Section 10.4.1 Inference as Decision

Section 10.4.1 Inference as Decision. AP Statistics March 4, 2010 CASA. When inference is used to make a decision…. Either you reject H 0 or you fail to reject H 0 . You can reject H 0 correctly You can fail to reject H 0 correctly You reject H 0 incorrectly (Type I error)

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Section 10.4.1 Inference as Decision

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  1. Section 10.4.1Inference as Decision AP Statistics March 4, 2010 CASA

  2. When inference is used to make a decision… • Either you reject H0 or you fail to reject H0. • You can reject H0 correctly • You can fail to reject H0 correctly • You reject H0 incorrectly • (Type I error) • You can fail to reject H0 incorrectly • (Type II error)

  3. Potato Chips Example • The salt content of the chips should have a mean of 2 mg with a standard deviation of .1 mg. • When deciding whether to accept or reject a batch of potato chips, a company looks at the salt content of 50 chips. • If the salt content is too far away from the mean, it will reject the batch.

  4. What range values are acceptable? • The company will check a 50 chip sample. • If our alpha is .05, the acceptable range is the same as the 95% confidence interval:

  5. We understand with normal variation and everything working normally, we will get a sodium value between 1.9723 mg and 2.0277 mg 95% of the time. Accept or reject?

  6. We understand with normal variation and everything working normally, we will get a sodium value between 1.9723 mg and 2.0277 mg 95% of the time. This means the 5% of the time you will reject a batch of chips that are fine. When we reject the batch (and H0) incorrectly we have committed a Type I error. Accept or reject?

  7. Accept H0 Reject H0 Reject H0 95% Confidence Interval 1.9723 2.0277

  8. Significance and Type I Error • The significance level α of any fixed level test is the probability of a Type I error. That is, α is the probability that the test will reject the null hypothesis H0 when H0 is in fact true.

  9. Probability of reject H0 correctly • The probability that we correctly reject H0 (that is, we say there is a difference when the difference really exists) is called the “Power”. • The probability of the Type II error is 1- “Power” • We increase the “Power” by either increasing • the sample size • Alpha • Remember, when we increase alpha, we increase the probability of the Type I error

  10. Assignment • 10.66-10.69 all

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