Question

Researchers would like to test if the mean bone mineral density is different for the three different groups. Conduct an ANOVA test to determine if there is a difference in the means of the 3 groups. Use a level of significance of LaTeX: \alpha = 0.05α = 0.05. What are the null and alternative hypotheses?

Answer 1

H₀: μ₁ = μ₂= μ₃

Hₐ: At least one of the means is different.

Explanation:

Analysis of variance or ANOVA test is used to determine whether the means of different groups are similar or not.

The hypothesis of an ANOVA test for n homogeneous groups is:

`H_(0): \mu_(1)= \mu_(2)= \mu_(3)...= \mu_(n)\\H_(a): At\ least\ one\ of\ the\ means\ is\ different`

In this case the researcher is testing whether the mean bone mineral density is different for the three different groups.

The hypothesis for this test can be defined as follows:

H₀: The mean bone mineral density is not different for the three different groups, i.e. μ₁ = μ₂= μ₃

Hₐ: The mean bone mineral density is different for the three different groups, i.e. at least one of the means is different.