1. 1 Where we are going : a graphic: Hypothesis Testing. 1 2 Paired 2 or more Means Variances Proportions Categories Slopes Ho: / CI Samples Ho: / CI Ho: Ho: / CI

2. 2 One Sample: Hypothesis testing. population sample Gather data Make inferences and comparisons parametersstatistics

3. 3 Hypothesis testing: 8 steps (briefly): 1. Research hypothesis (Ha:). 2. Null hypothesis (Ho:). 3. A. State type I error. B. State type II error. 4. State , (the probability of type I error). 5. Draw the rejection region; state rejection criterion. 6. Compute the test statistic. 7. Make a decision about Ho:. 8. State a conclusion. These will be explained in the context of examples.

4. 4 An hypothesis about the mean. (Pulse rate example). Consider that we are interested in knowing if average 15 second pulse rate is different than 20. It has been shown that in statistics classes, if average pulse rate is different from 20, a large portion of students are thinking about something else and retention of material is low. At this point, students need to be jolted somehow to regain consciousness. Is a jolt needed ? 1. Research (alternate) hypothesis: Ha:  ≠ 20. 2. Null hypotheses: Ho:  = 20. 3. A. Type I error: Claim pulse rate is different than 20 when in fact it is not (reject Ho|Ho is true). B. Type II error: Claim pulse rate is equal to 20 when in fact it is not (accept Ho|Ho is false).

5. 5 An hypothesis about the mean, continued, 1. 4. Type I error tolerated: let  =.05. 5. Rejection Region:.025.025 t  /2,(n-1) = t.025,127 = -1.96 1.96 Reject Ho if t obs is less than -1.96. or if t obs is greater than 1.96. 6. Test statistic:

6. 6 An hypothesis about the mean, continued, 2. At this point, an experiment is conducted and data are collected. The following are the results: 128 measurements on 15 second pulse rate were made. the mean was 19.60 and the standard deviation was 2.24. So: 6. 7. Decision: Since -2.02 < -1.96, Reject Ho: (plot -2.02 on the drawing in 5) in favor of Ha:.

7. 7 An hypothesis about the mean, continued, 3. 8. Conclusion. A recent study of 128 randomly selected students showed that average 15 second pulse rate is lower than 20. A jolt back to consciousness seems to be necessary. What would you suggest ? We are 95% certain our answer is correct; or, there is a 5% chance we have rejected incorrectly. If the null is in fact correct, 5 out of 100 studies done in this way will lead to rejection.

8. 8 Three kinds of research/null hypotheses: Rejection region for t: I. Ha:  <  o  Ho:    o 0 II. Ha:  >  o  Ho:    o 0 III. Ha:    o  /2  /2 Ho:  =  o 0