Types of Hypothesis Tests Examples ad nauseum...

One-Sample Mean Population of Penn State students Sample of 1000 students Is , average number of unwanted pregnancies, 0.02? How likely would sample have average as extreme as 0.01 if  = 0.02?

One-Sample Mean H 0 :  = 0.02 versus H A :   0.02 Reject if P-value is small.

Two-Sample Independent Means Population of Male Penn State Students Population of Female Penn State Students Does  M, avg. number of condoms purchased monthly by males, differ from  F, avg. number of condoms purchased monthly by females? Sample of 50 Male students Sample of 50 Female students Calculate sample difference.

Two-Sample Independent Means H 0 :  M =  F versus H A :  M   F H 0 :  M -  F = 0 versus H A :  M -  F  0 How likely would two samples have difference as extreme as 2 condoms if  M -  F = 0, that is, if there is no difference in populations? Reject if P-value is small.

Paired Means Population of male students before unwanted pregnancy Same pop’n of male students after unwanted pregnancy Is  B, avg. number of condoms purchased monthly before pregnancy less than  A, avg. number of condoms purchased monthly after pregnancy? Sample of 50 such males Calculate sample difference.

Paired Means H 0 :  A =  B versus H A :  A >  B H 0 :  A -  B = 0 versus H A :  A -  B > 0 How likely would sample have difference as extreme as 10 condoms if  A -  B = 0, that is, if there is no difference in the means? Reject if P-value is small.

One-Sample Proportion Population of statistics students Sample of 300 students Is p, proportion of students who like their statistics course, 0.20? How likely would sample have proportion as extreme as 0.80 if p = 0.20?

One-Sample Proportion H 0 : p = 0.20 versus H A : p  0.20 Reject if P-value is small. Use sample proportion to calculate P-value.

Two-Sample Independent Proportions Population of Male Penn State Students Population of Female Penn State Students Does p M, proportion of males who practice religion, differ from p F, proportion of females who practice religion? Sample of 500 Male students Sample of 500 Female students Calculate sample difference.

Two-Sample Independent Proportions H 0 : p M = p F versus H A : p M  p F H 0 : p M - p F = 0 versus H A : p M - p F  0 How likely would two samples have difference as extreme as 0.07 if p M - p F = 0, that is, if there is no difference in populations? Reject if P-value is small.

Relative Risk Population of binge drinking college students Population of non-binge drinking college students Is p B, percentage of binge drinkers who become alcoholic larger than p N, percentage of non-binge drinkers who become alcoholic? Sample of 500 binge drinkers Sample of 500 non-binge drinkers Calculate sample difference.

Relative Risk H 0 : p B = p N versus H A : p B  p M H 0 : RR = 1 versus H A : RR  1 How likely would two samples produce relative risk as large as 1.75 if population relative risk were 1? Reject if P-value is small.

What to learn? How to distinguish between, and set up, different hypotheses. How to read scientific reports on results of hypothesis tests. How to calculate, or how to ask Minitab, to calculate P-values for various hypothesis tests.