1. We’ve learned:

2. What’s next We will look at some examples and you can guess!

3. Hypotheses (Engineer) Two different types of polishing solution are being evaluated for possible use in a tumble-polish operation for manufacturing intraocular lenses used in the human eye following cataract surgery. p 1 = proportion of defects using the first polishing solutions p 2 = proportion of defects using the second polishing solutions Is there any reason to believe that the two polishing solutions differ? a) H 0 : p 1 = p 2, H a : p 1 ≠ p 2 b) H 0 : p 1 = p 2, H a : p 1 > p 2 c) H 0 : p 1 = p 2, H a : p 1 < p 2

4. Hypotheses (Biology) Does hormone replacement therapy cause increased risk of invasive breast cancer? p 1 = proportion of women taking HRT who get invasive breast cancer p 2 = proportion of women not taking HRT who get invasive breast cancer a) H 0 : p 1 = p 2, H a : p 1 ≠ p 2 b) H 0 : p 1 = p 2, H a : p 1 > p 2 c) H 0 : p 1 = p 2, H a : p 1 < p 2

5. Hypotheses (Ecology) How do we estimate an animal population's size in ecology study? A portion of the population is captured, marked, and released. Later, another portion is captured and the number of marked individuals within the sample is counted. p 1 = portion counted from recapture. p 2 = repeat this action in a later time Is the population decreasing? a) H 0 : p 1 = p 2, H a : p 1 ≠ p 2 b) H 0 : p 1 = p 2, H a : p 1 > p 2 c) H 0 : p 1 = p 2, H a : p 1 < p 2

6. Inference for two population proportions Assumptions:

7. Slight change than one proportion test

8. Test procedures

9. Test procedures con’t

11. Example