A Closer Look at Testing

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Presentation transcript:

A Closer Look at Testing Section 4.4 A Closer Look at Testing

Review The p-value of a hypothesis test is 0.02. Using α = 0.05, we Reject H0 Do not reject H0 Reject Ha Do not reject Ha The p-value is less than α, so we reject H0

A new blood thinning drug is being tested against the current drug in a double-blind experiment. Is there evidence that the mean blood thinness rating is higher for the new drug? Using n for the new drug and o for the old drug, which of the following are the null and alternative hypotheses? A. H0: n > o vs Ha: n = o B. H0: n = o vs Ha: n  o C. H0: n = o vs Ha: n > o H0: vs Ha:

A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H0: n = o vs Ha: n > o What does a Type 1 Error mean in this situation? We reject H0 We do not reject H0 We find evidence the new drug is better when it is really not better. We are not able to conclude that the new drug is better even though it really is. We are able to conclude that the new drug is better.

A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H0: n = o vs Ha: n > o What does a Type 2 Error mean in this situation? We reject H0 We do not reject H0 We find evidence the new drug is better when it is really not better. We are not able to conclude that the new drug is better even though it really is. We are able to conclude that the new drug is better.

Probability of Type I Error How can we reduce the probability of making a Type I Error (rejecting a true null)? Decrease the significance level Increase the significance level

Probability of Type II Error How can we reduce the probability of making a Type II Error (not rejecting a false null)? Decrease the significance level Increase the significance level

H0: n = o vs Ha: n > o A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H0: n = o vs Ha: n > o If the new drug has potentially serious side effects, we should pick a significance level that is: Relatively small (such as 1%) Middle of the road (5%) Relatively large (such as 10%) Since a Type 1 error would be serious, we use a small significance level.

H0: n = o vs Ha: n > o A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H0: n = o vs Ha: n > o If the new drug has no real side effects and costs less than the old drug, we might pick a significance level that is: Relatively small (such as 1%) Middle of the road (5%) Relatively large (such as 10%) Since a Type 1 error is not at all serious here, we might use a large significance level.

Probability of Type II Error How can we reduce the probability of making a Type II Error (not rejecting a false null)? Decrease the sample size Increase the sample size