Question

Part A: Which of the following is most accurate?

A. MS error estimates the error variance only when the null hypothesis is true.

B. MS treatment estimates the error variance only when the null hypothesis is true.

C. None of above.

D If the ratio of MS treatment and MS error is close to one, we reject the null hypothesis.

Part B:

What does rejecting the null hypothesis imply in a one-way ANOVA assuming k groups?

1. There is no difference in any pair of population means.

B. The population means are equal to a known population mean.

C. Each population mean differs significantly from every other population mean.

D. Some subset of population means significantly differs from some other subset of population means.

Answer 1

Ans:

1)Option B is correct.

MS treatment(i.e. Mean square between) estimates the error variance only when the null hypothesis is true.

Mean Square Between is based on the variance of the sample means. The MSB is only an estimate of σ² if the null hypothesis is true. If the null hypothesis is false then MSB estimates something larger than σ².

2)Option D is correct.

Some subset of population means significantly differs from some other subset of population means.