1) Inference on population mean , variance is known ( Z-test )( large sample size or assume population is normal )

2) Inference on population mean , variance is unknown ( T-test )( large sample size or assume population is normal )

3) Inference on population proportion ( Z-test )( need large sample size )

4) Inference on variance of a normal population ( chi-square test) ( Assume population is normal)

We’ve learned:

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

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.

p1 = proportion of defects using the first polishing solutions

p2 = proportion of defects using the second polishing solutionsIs there any reason to believe that the two polishing solutions differ?

a) H0: p1= p2, Ha: p1≠ p2

b) H0: p1= p2, Ha: p1> p2

c) H0: p1= p2, Ha: p1< p2

Hypotheses (Biology)Does hormone replacement therapy cause increased risk of invasive breast cancer?

p1 = proportion of women taking HRT who get invasive breast cancerp2 = proportion of women not taking HRT who get invasive breast cancer

a) H0: p1= p2, Ha: p1≠ p2

b) H0: p1= p2, Ha: p1> p2

c) H0: p1= p2, Ha: p1< p2

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.

p1 = portion counted from recapture.p2 = repeat this action in a later time

Is the population decreasing?

a) H0: p1= p2, Ha: p1≠ p2

b) H0: p1= p2, Ha: p1> p2

c) H0: p1= p2, Ha: p1< p2

Inference for two population proportionsAssumptions:

Slight change than one proportion test

Test procedures

Test procedures con’t

Test procedures con’t

Example