# Null and alternative hypothesis for testing means of three groups

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For the use of a one-way ANOVA there must be more than two means that are being compared. As a result, the following research question is proposed: Does a six week or 12 week self-monitoring program provided to teens between the ages of 13 and 15 diagnosed with ADHD reduce anxiety levels when compared with no intervention?

In order to answer this question, three different groups will be needed: teens between the ages of 13 and 15 diagnosed ADHD provided with the intervention for six weeks, teens between the ages of 13 and 15 diagnosed ADHD provided with the intervention for 12 weeks, and teens between the ages of 13 and 15 diagnosed ADHD provided with no intervention. This question makes many of the same assumptions that are integral to the use of the independent samples t-test. Specifically, the question assumes that the sample sizes will be equal, the variances will be similar, and the dependent value is from a normally distributed population. The principle difference with this research question is that there are three means that must be compared in order to answer the research question. Based on this reality, the one-way analysis of variance provides the most effective tool for determining if there are any statistically significant differences in the population.

My Research Hypothesis: In teens between the ages of 13 and 15 that have been diagnosed with ADHD, a self-monitoring program provided for 12 weeks will help reduce anxiety as measured by the Beck Anxiety Inventory (BAI) compared with teens that receive the intervention for six weeks or do not receive the intervention at all.

Null Hypothesis: A self-monitoring intervention provided for 12 weeks will have no impact on anxiety levels as measured by the BAI for teens between the ages of 13 and 15 diagnosed with ADHD compared with teens that receive the intervention for six weeks or do not receive the intervention at all.

Alternative Hypothesis: There will be a statistically significant difference in anxiety scores on the BAI for teens between the ages of 13 and 15 diagnosed with ADHD who receive either a 12 week or six week self-monitoring program compared with teens that do not receive the intervention.

Question: I am doing a one way ANOVA hypothesis test. In a short version is this the correct way to statistically write my null hypothesis and alternative hypothesis without writing all the words that have in my null and alternative hypothesis?

Ha: μ1 = μ2 = μ3: mean total points Group1 = mean total points Group2 = mean total points Group3

Ha: μ1≠ μ2 ≠ μ3 : mean total points Group1 ≠ mean total points Group2 ≠ mean total points Group3

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##### Solution Summary

The solution gives accurate statements for null and alternative hypotheses on testing means of three groups.

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First, we need to define μ1, μ2 and μ3. Let u1 be mean score of groups of teens between the ages of 13 and 15 diagnosed ADHD provided with the intervention for six ...

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