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An investor with a stock portfolio worth several hundred thousand dollars sued 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 an arbitration panel. The arbitration panel compared a sample of 39 months of the investor's returns with the average of the Standard & Poor's 500-stock index for the same period in order to determine whether there was a substantial decrease. Their data:

-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

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Suppose that you are a member of this arbitration panel. Construct a 95% confidence interval for the true mean return of the investor's portfolio. 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 three decimal places.