Question

Study of mutual fund performance. Mutual funds are classified as large-cap funds, medium-cap funds, or small-cap funds, depending on the capitalization of the companies in the fund. Hawaii Pacific University researchers investigated whether the average performance of a mutual fund is related to capitalization size (American Business Review, January 2002). Independent random samples of 30 mutual funds were selected from each of the three fund groups, and the 90-day rate of return was determined for each fund. The data for the 90 funds were subjected to an analysis of variance, with the results shown in the ANOVA summary table below.

a. State the null and alternative hypotheses for the ANOVA.

Short answer

a. The hypothesis are given by

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3}\)

\({H_a}:{\mu _1} \ne {\mu _2} \ne {\mu _3}\).

Step-by-step solution

Given Information

The three mutual funds are given.

So, there are three treatments which are large-cap funds, medium-cap funds, and small-cap funds.

Random samples of 30 mutual funds were drawn from the three fund groups.

Specifying the null hypothesis

The null hypothesis are given by

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3}\)

That is all treatments are equal.

Specifying the alternative hypothesis

The alternative hypothesis are given by

\({H_a}:{\mu _1} \ne {\mu _2} \ne {\mu _3}\)

That is at least two treatments are not equal.