SOLUTION: You have 7 means, and you want to compare each mean to every other mean. (a) How many tests total are you going to compute? (b) What would be the chance of making at least o

Question 1086020: You have 7 means, and you want to compare each mean to every other mean.
(a) How many tests total are you going to compute?
(b) What would be the chance of making at least one Type I error if the Type I error for each test was .05 and the tests were independent?
(c) Do you think the chance of making at least one Type 1 error when comparing these 7 tests is high or low? Explain your answer.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is 7C2=21 different tests. It is how many ways to choose 2 items from 7. It is 7!/5!2!
The chance of a Type I error is 0.05. The chance of not making one is 0.95, which is 1-0.05.
The chance of not making ANY Type I errors in 21 trials is 0.95^21. But I want to know what is the probability of making at least 1. That is 1-0.95^21.
.95^21=0.341=the probability of not making a Type I error, and a 0.659 probability of making at least one.
Even assuming some dependence in the tests, there is a much higher likelihood than desired that a Type I error will be made. Certainly, it won't be 5%.
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