1. 1 of 7 Exercise 4 Hypothesis Testing: Beta Error 30 minutes Presenter: Sebastian Tindall DQO Training Course Day 2

2. 2 of 7 Exercise 4 For this Exercise, the Action Level is still set at 7 ppm. However, for this Exercise the True Mean for this bag of beads is now set at 6 ppm. This is done by having the students ignore any Dark Green (13 ppm) and Black beads (14 ppm) they select when sampling. The LBGR is also set to 6 ppm. Therefore, the True Mean = LBGR. Now, “This site is Clean”.

3. 3 of 7 Exercise 4 (contd.) Take a new random sample of n = 5 beads. Ignore all Dark Green (13 ppm) and Black beads (14 ppm). Select again for each Dark Green or Black bead you select. Provide your sample values to the instructor for spreadsheet calculations. Note: no values of 13 or 14 should be provided to the instructor. Calculate your 95% UCL Your 95% UCL = Check: Based on the UCL, your site is: “Clean”_____ or “Dirty” _____

4. 4 of 7 Exercise 4 (contd.) The current test is 95% UCL on x-bar >= AL implies “dirty,” otherwise site is “clean”. Record the number of sites that the class declared “dirty” below and calculate the Beta error rate for the class: Number “dirty” Decisions --------------------------------- = ------------------------------ X 100 = Total Number of Decisions

5. 5 of 7 Exercise 4 (contd.) Draw in a blue dot on LBGR line of your DPGD at the Beta error % Why is the class Beta error so high?

6. 6 of 7 Exercise 4 (contd.) The computer will simulate the sampling and evaluate the Beta error. Students will discuss whether 5 or 50 samples are sufficient to make correct decisions within the alpha error rate.

7. 7 of 7 End of Exercise 4 Thank you Questions? This concludes our presentation for Day 2 See you here at 8:00 AM tomorrow for Day 3. Please complete the Day 2 Evaluation Form.