Inference Concepts Hypothesis Testing

An Example A research paper claims that the mean fetal heart rate is 137 bpm. A doctor feels that the mean rate is lower for women admitted to her clinic. What are the statistical hypotheses? HA: m < 137 HO: m = 137 She will test her belief with … a random sample of 100 patients assuming s =10 Inference Concepts

The Null Hypothesis Assumed, initially, to be true Used to predict what will be observed in a sample Thus, if H0: m=137 then one predicts that`x=137 IF there was no sampling variability, then what do you think about H0 if`x=135 is observed Draw the null sampling distribution … put on three possible x-bars and ask what that means about mu. Inference Concepts

Objectivity – p-value PR(observed statistic or value more extreme assuming H0 is true) shade to left if a “less than” HA shade to right if a “greater than” HA shade into both tails if a “not equals” HA One-Tailed Suppose that xbar=135.9. Compute p-value (including showing the definition in the context of this example). Two-Tailed Inference Concepts

Objectivity – p-value Critical Compare to rejection criterion – a PR(observed statistic or value more extreme assuming H0 is true) Critical Compare to rejection criterion – a if p-value < a then reject H0 if p-value > a then Do Not Reject (DNR) H0 Rejection criterion (a) “sets” cut-off value for determining support of H0 Set by researcher a priori typical values are 0.10, 0.05, 0.01 Explain what the previous p-value means Inference Concepts