Question

Suppose a researcher is performing a CR-3 design. Further suppose the P value for the testing the means is 0.0123. What conclusion can be made.

There is enough evidence to conclude that all the means are equal

There is not enough evidence to conclude that any of the means differ

There is not enough evidence to conclude all the means are different

There is enough evidence to conclude that all the means are different

There is enough evidence to conclude that not all the means are equal and further testing must be done to determine which means differ

Answer 1

Given a p-value of 0.0123 and a significance level (alpha) of 0.05, there is enough evidence to reject the null hypothesis, indicating that not all group means in the CR-3 design are equal, and further testing is needed to specify which means differ.

Step-by-step explanation:

The student is inquiring about the conclusion of a hypothesis test within the context of a Completely Randomized Design (CRD), specifically a CR-3 design which generally suggests a comparison of means among three groups. Given that the p-value is 0.0123, this is compared to a commonly used alpha level of 0.05. Since the p-value is lower than the alpha level, the correct decision is to reject the null hypothesis. Therefore, there is enough statistical evidence to conclude that not all the group means are equal in the CR-3 design experiment. However, this conclusion only tells us that at least two means are significantly different, but further testing (such as post hoc comparisons or multiple comparisons procedures) is needed to determine which specific group means differ from each other.