Final answer:
The alternative hypothesis (Ha) in a one-way ANOVA with a significant test statistic suggests that at least two of the group means are significantly different, indicating that not all the treated populations have the same mean performance.
Step-by-step explanation:
When you obtained a significant test statistic in a one-way ANOVA, the interpretation of the alternative hypothesis (Ha) would be that not all group means are equal. Specifically, the alternative hypothesis suggests that there is at least one pair of group means that are significantly different from each other. In other words, Ha posits that there is a difference in mean performance across the three treatments. This means that the means of the treatments (represented as μ1, μ2, and μ3) are not all equal and mathematics would usually represent this as μᵢ ≠ μᵣ for some i ≠ j.
The one-way ANOVA test determines if multiple population means are equal and uses the F distribution for the test statistic. A significant test statistic leads us to reject the null hypothesis which states that all group means are equal. The alternative hypothesis is the hypothesis that is considered when the null is rejected, and in the context of ANOVA, it suggests that there is variance among the means that is unlikely due to chance alone.