Final answer:
The mean square error (MSE) is a good estimate of the population variance when the null hypothesis is true, as it accounts for variability within and between samples.
However, when the null hypothesis is false, MSE may not accurately estimate the population variance.
Therefore, the correct answer is: option B). When the null hypothesis is true.
Step-by-step explanation:
In statistics, the mean squared error or mean squared deviation of an estimator measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss.
When the null hypothesis is true, MSE provides a good estimate of the population variance. This is because the null hypothesis assumes that all group populations have the same normal distribution, and MSE accounts for the variability within and between the samples.
On the other hand, when the null hypothesis is false, MSE may not be an accurate estimate of the population variance. In this case, the mean square between groups (MSbetween) will generally be larger than the mean square within groups (MSwithin), resulting in an F ratio larger than 1.