In one-way ANOVA involving three groups, the alternative hypothesis would be considered correct if, in the population,
a. all means were equal.
b. two means are equal but the third is different.
c. all three means have different values.
d. either (b) or (c) above is true.
D. Either (b) or (c).
To determine the correct alternative hypothesis in a one-way ANOVA involving three groups, we need to understand the purpose of the ANOVA and its underlying assumptions.
The one-way ANOVA is used to test the null hypothesis that the means of all groups are equal against the alternative hypothesis that at least one mean differs from the others. In this case, the null hypothesis states that all means are equal (option a). Therefore, the alternative hypothesis (option d) would be considered correct if either option b or option c is true.
Option b states that two means are equal, but the third is different. This means that there is at least one group whose mean is different from the other two groups. This scenario supports the alternative hypothesis.
Option c states that all three means have different values. If this is true, it implies that all three groups have distinct mean values, which also supports the alternative hypothesis.
So, the correct answer is option d, either (b) or (c) above is true.