An investor with a stock portfolio worth hundreds of thousand of dollars sues his broker and brokerage firm because he felt that lack of diversification in his portfolio led to poor performance for many years in a row. In an effort to avoid close public scrutiny, the firm agreed to settle the conflict by arbitration panel. The arbitration panel compared a sample of 39 months of the investor's returns with the average of the Standard & Poor 500 stock index for the same period in order to determine whether there was a substantial decrease. Their data is in the file ratesofreturn.xlsx.
Monthly RoR -8.63 6.82 -9.16 -0.65 -2.14 1.63 -2.35 -1.25 4.34 -1.01 -2.27 -3.58 -1.22 12.22 -1.41 -2.93 6.13 -10.27 -7.21 12.03 -2.70 7.00 -5.11 -0.09 -2.56 -2.93 -15.25 -0.80 7.34 4.33 -9.14 -8.66 -1.44 5.04 2.35 -2.64 -1.03 1.28 -7.24
Suppose that you are a member of the arbitration panel, Construct a 95% confidence interval for the true mean return of the investor's portfolio. Record you answers below:
1) Find the margin of error for the 95% confidence interval for the true mean return of the investor's portfolio. Round your answer accurate to 3 decimal places.
2) Input the lower bond of your confidence interval (round your answer accurate to 3 decimal places.)
3) Input the upper bound of your confidence interval. (round your answer accurate to 3 decimal places.)
4) Historically, the S&P has a mean return of 0.95 Conduct a hypothesis test to determine if the investor's portfolio performed significantly worse than the performance of the S&P 500. Use a level significance of a=0.05 Is it one tailed or two tailed?
5) What is the t-score fr this test? (round your answer accurate to 3 decimal places.)
6) What is the p-value of this test? (round your answer accurate to 3 decimal places.)
7) Based on the results of this test, is there enough evidence to say that the investor's portfolio performed significantly worse than the S&P 500?
*Yes, because we rejected the null.
*Yes, because we failed to reject the null
*No, because we rejected the null
*No, because we failed to reject the null