# Question: This exercise motivates the formula for the between subjects estimate of

This exercise motivates the formula for the between-subjects estimate of the variance in one-way ANOVA. Suppose each population mean equals μ (that is, H0 is true) and each sample size equals n. Then the sampling distribution of each i has mean μ and variance σ2/n, and the sample mean of the i values is the overall sample mean, {}.

a. Treating the g sample means as g observations having sample mean , explain why Σ (i - )2 / (g - 1) estimates the variance σ2/n of the distribution of the {i} values.

b. Using part a, explain why the between-groups estimate Σ n (i - )2 / (g - 1) estimates σ2. (For the unequal sample size case, the formula replaces n by ni.)

a. Treating the g sample means as g observations having sample mean , explain why Σ (i - )2 / (g - 1) estimates the variance σ2/n of the distribution of the {i} values.

b. Using part a, explain why the between-groups estimate Σ n (i - )2 / (g - 1) estimates σ2. (For the unequal sample size case, the formula replaces n by ni.)

**View Solution:**## Answer to relevant Questions

The Bonferroni theorem states that the probability that at least one of a set of events occurs can be no greater than the sum of the separate probabilities of the events. For instance, if the probability of an error for each ...A study about smoking and personality used a sample of 1638 adults in the Baltimore Longitudinal Study on Aging. The subjects formed three groups according to smoking status (never, former, current). Each subject completed a ...Refer to the previous exercise. The analysis there did not take into account the size of the change in blood pressure. Show how to do this with the Wilcoxon signed-ranks test. a. State the hypotheses for that test, for the ...Examples 1 and 2 compared two methods of getting a tan. Suppose Allison conducted an expanded experiment in which nine participants were randomly assigned to one of two brands of tanning lotion or to the tanning studio, ...For the tanning experiment, Table 15.2 showed the sampling distribution of the difference between the sample mean ranks. Suppose you instead use as a test statistic the sample proportion of pairs of participants for which ...Post your question