An investor recorded the performance of stock mutual funds during the last 3 years 2020, 2021, and 2022 and classified the stock mutual funds into three categories: growth, income, and mixed. As part of the experiment, he observed the rate of return (\%) of 36 randomly selected stock mutual funds classified into equal groups by Year and Type of Stock which are given in the following table. He would like to test whether the rate of return of the stock is affected by the factors Type of Stock and Year. (a) [4] Identify the experimental design, number of factors along with levels, number of treatments, and number of replications. (b) [4.5] Do the data provide sufficient evidence to indicate an interaction between type of stock mutual fund and year? Conduct an appropriate test of hypothesis at 5% level of significance using both critical value and p-value approach. Please provide hypotheses, test statistic, critical value, p-value, decision with justification. (STATCRUNCH) (c) [3] Test at 5% level of significance the difference in average rate of return among three types of stock mutual funds using critical value approach. (STATCRUNCH) \begin{tabular}{|l|r|l|} \hline Type & 1 & Growth \\ \hline & 2 & Income \\ \hline & 3 & Mixed \\ \hline Year & & \\ \hline & 1 & 2020 \\ \hline & 2 & 2021 \\ \hline & 3 & 2022 \\ \hline \end{tabular}