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Exercise 4

DQO Training Course Day 3. Exercise 4. Hypothesis Testing: Beta Error. Presenter: Sebastian Tindall. (30 minutes). 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.

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Exercise 4

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  1. DQO Training Course Day 3 Exercise 4 Hypothesis Testing: Beta Error Presenter: Sebastian Tindall (30 minutes)

  2. 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. 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. 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. 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. 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. End of Exercise 4 Thank you Questions?

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