Suppose we want to test whether or not three population means are equal. We can assume the population variances are equal and there is only one factor of difference. We want to perform this test with a 10% significance level.

1)If we perform an ANOVA test, what is the probability of the test producing accurate results (avoiding a Type I error)?

Suppose we, instead, run three separate hypothesis tests (t-tests), each with 10% significance level.

• • Mean 1 = Mean 2
  • Mean 1 = Mean 3
  • Mean 2 = Mean 3

2)What is the probability that all three tests would be accurate? Hint: use principles of probability to help your calculations: P(accurate AND accurate AND accurate)?

3)Why would we use ANOVA instead of three separate tests?

4)Why would we want to use three separate tests instead of ANOVA?

*Please answer all questions separately. Thanks