You obtained a significant test statistic when comparing three treatments in a one-way ANOVA. In words, how would you interpret the alternative hypothesis Ha?None of 1., 2. and 3.All of 1., 2. and 3.2.Exactly two of the three treatments have the same effect on the mean response.3.At least two treatments are different from each other in terms of their effect on the mean response.1.All three treatments have different effects on the mean response.
Question
You obtained a significant test statistic when comparing three treatments in a one-way ANOVA. In words, how would you interpret the alternative hypothesis Ha?None of 1., 2. and 3.All of 1., 2. and 3.2.Exactly two of the three treatments have the same effect on the mean response.3.At least two treatments are different from each other in terms of their effect on the mean response.1.All three treatments have different effects on the mean response.
Solution
The alternative hypothesis (Ha) in a one-way ANOVA is that at least one of the group means is different from the others. In the context of your question, this would mean that at least one of the treatments has a different effect on the mean response.
So, if you obtained a significant test statistic, this would suggest that you reject the null hypothesis (that all treatments have the same effect) in favor of the alternative hypothesis.
In terms of the options you provided:
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"All three treatments have different effects on the mean response." - This could be true, but the alternative hypothesis doesn't necessarily specify that all treatments are different, just that at least one is.
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"Exactly two of the three treatments have the same effect on the mean response." - This could also be true, but again, the alternative hypothesis doesn't specify this exactly. It could be that two treatments are the same and one is different, or that all three are different.
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"At least two treatments are different from each other in terms of their effect on the mean response." - This is the most accurate interpretation of the alternative hypothesis. If you have a significant result, it suggests that at least two of the treatments have different effects on the mean response.
So, the best answer would be "At least two treatments are different from each other in terms of their effect on the mean response."
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