1. We will display the rates of return for the two types of funds with histograms and examine the rate of return for each stock expressed as the proportional change in price of the stock over a one year period. (a) Obtain frequency histograms of rate of return for the no-load and load funds. Use the class intervals of width 5 with bins beginning at -40 and going to 30. Each histogram should have a title, labels at the axes, borders around the bars, and no gaps between the bars. Paste the histograms into your report. (b) Describe the shapes of the two distributions. In particular, compare the centers, spreads and skewness of the two distributions. Are there are any outliers in either group? (c) Use the Descriptive Statistics tool to obtain the summaries of the rate of return for the no-load and load funds. Paste the summaries into your report. How much did the funds lose or gain in 2002, on average? Compare their standard deviations. (d) What were the best and the worst-performing funds in the two samples? 3. Now you will compare the mean returns for the No-Load funds and the Load funds. (a) Is there evidence that there is a difference in rates of return for the two types of funds? Answer the above question by carrying out the appropriate test in Data Analysis at the level of significance =0.05. Before you choose an appropriate test, you might refer to the summaries in Question 1 to decide whether the test with the assumption of equal variances would be more appropriate than the test without the assumption. Refer to the rules discussed in class to decide. State the null and alternative hypothesis and the distribution of the test statistic under the null hypothesis. Report the value of the test statistic provided by Excel, the p-value, and your conclusion. Paste the output into your report. Would the outcome of the tests for the level a=0.01 be the same? Explain briefly. (b) Obtain a 95% confidence interval for the mean difference in rates of return for the two funds. You may use the summaries obtained in Question 1 and the variance in the output in part (a) to construct the interval. State your conclusion. (c) Compare the confidence interval in part (b) with the outcome of the test in part (a). Are the two conclusions consistent? Explain referring to the theory. (d) State the assumptions to make the inferences in parts (a) and (b) valid. Is there evidence that any of the assumptions may be violated for the data? You may refer to the histograms obtained in Question 1 to answer the question.