The following is a description of the numerical variables in the file: Description of Variable NOLOAD Rate of return for no-load funds, PNOLOAD LOAD Projected rate of return for no-load funds, Rate of return for load funds. Answer the following questions: 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? a) Histogram of no Load Funds Rates of Return Frequency Frequency 8 7 5 2 1 0 -40 rate of return for no-load funds 25 More Frequency 14 Histogram of Load Funds Rates of Return 12 10 8 6 4 2 0 08 SE S rate of return for load funds ST 25 More Frequency 0 NOLOAD LOAD Mean -9.78974359 Mean -14.92156863 Standard Error 2.047383356 Standard Error 1.409628831 Median Mode -10 Median -2.9 Mode -15.5 -15.5 Standard Deviation 12.78590496 Standard Deviation 10.06676341 Sample Variance 163.4793657 Sample Variance 101.3397255 Kurtosis -0.09582053 Kurtosis 0.992829043 Skewness Range Minimum -0.053413666 Skewness 54.4 Range -35.4 Minimum 0.788084261 50.4 -34 Maximum 19 Maximum 16.4 Sum -381.8 Sum -761 Count 39 Count 51 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 a=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. a. HO: the mean of the rate of return is the same between no load funds and load funds Ha: the mean of the rate of return is different between no load funds and load funds t-Test: Two-Sample Assuming Equal Variances NOLOAD LOAD Mean -9.7897 -14.9216 Variance 163.4794 101.3397 Observations 39.0000 51.0000 Pooled Variance 128.1728 Hypothesized Mean Difference 0.0000 df 88.0000 t Stat 2.1309 P(T b. formula: mu_noload-mu_load pm t*s_pooled *sqrt(1/n1+1/n2) mu_noload-mu_load t s_pooled sqrt(1/n1+1/n2) Cl upper Cl lower 5.1318 1.9873 11.3213 0.2127 9.9177 0.3459