Question

The null hypothesis for an ANOVA is that all treatments/samples come from populations with the same mean. The alternative hypothesis is best stated as: "" of the population means is different from the others.

Answer 1

Answer:

Alternative hypothesis: "AT LEAST ONE" of the population means is different from the others

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

If we assume that we have n groups and we want to check if the population means are equal, th best way to check this it's with an ANOVA test.

The hypothesis for this case are:

Null hypothesis: $\mu_{1}=\mu_{2}=\dots =\mu_{n}$

Or in words:

Null hypothesis: All treatments/samples come from populations with the same mean

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=1.2,\dots ,n$

Or we can say:

Alternative hypothesis: "AT LEAST ONE" of the population means is different from the others