Question

Suppose we want to test whether or not three means are equal. We want to perform this test with a 7% significance level.

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 7% significance level.

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

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)________ (Write your answer accurate without rounding.)

Why would we use ANOVA instead of three separate tests?

____________________________________________________________________

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

_____________________________________________________________________

Answer 1

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

= 1-0.07

= 0.93

What is the probability that all three tests would be accurate?

= (1-0.07)^3

= 0.804357

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