We already know how to compare two means. When we have many means and want to determine if any of them are different we ...

  

We already know how to compare two means. When we have many means and want to determine if any of them are different we could simply test all possible pairs. Why is this not a good idea unless we take precautions? 

You are looking for diets that reduce blood cholesterol in rats. You created 20 test diets and did an experiment in which 4 randomly selected rats were fed each diet. Blood cholesterol was measured on each rat at the end of 30 days of feeding. Because you do this before knowing about ANOVA you decide to test for differences using the independent observations procedure for two population means, taking two diets at a time. You use alpha=0.05 for each test. Assume that the test are all independent.

 How many different tests of Ho: mu1=mu2 do you make? ____ 

What is the probability that you make a type I error in each test separately? ____ 

What is the probability that you make a type I error in just one of all the tests? ____ 

What is the probability that you make a type I error in NONE of the tests? ____

What is the probability that you make a type I error in at least one test? ____