Question

A low P-Value in ANOVA table mean that the population mean of each treatment effects are different. the population mean of at least one treatment effect are different. the population mean of at least one treatment effect are the same. the population mean of each treatment effects are the same.

Answer 1

The population mean of at least one treatment effect are different.

Explanation:

An analysis of variance (ANOVA) is conducted in order to determine if there are significant differences between the values of the population mean with respect to the response variable for the domains that under the effects of different treatments. A low p-value leads to reject the null hypothesis of the following hypothesis system:

`H_0: \mu_1=\mu_2=...=\mu_k\\\\\\H_a: \mu_i \\eq\mu_j, for $ for some i, j between 1 and k.$`

Rejecting H0 means that this hypothesis is false and, in turn, allows us to conclude that the population mean of one of the domains is different from the others.