Suppose there are 5,547 daily observations for the returns of stocks in the Fortune 500 portfolio. The portfolio average return is 0.0213 with a standard deviation of 0.7832.Formally state the hypothesis test on whether the return on the Fortune 500 portfolio is different from 0. Use a two-tailed test.Using the confidence interval method, test your hypothesis at the 90% confidence level. Explicitly state the results of the test.Using the t-test method, determine at which conventional significance levels you can reject the null hypothesis and refute your friend’s claim (if any).

Given information: Mean=0.0213S.D=0.7832n=55471) Perform the one sample t-test using the sample data. Null hypothesis: H0 : μ=0 Alternative hypothesis: HA: μ≠0 This hypotheses constitute a two-tailed test and significance level for the test is 0.05. Use the sample data to calculate the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t). S.E=S.Dn=0.78325547=0.010515831≈0.01052D.F=n-1=5547-1=5546 t=x-μS.E=0.0213 -00.01052=2.025517537≈2.03The P-value for this test is the probability that a t statistic having 5546 degrees of freedom is more extreme than -2.03; that is, less than -2.03 or greater than 2.03. P-value = P(t < -2.03) + P(t > 2.03) P-value = 2P(t > 2.03) Use the excel formula, "=T.DIST.2T(2.03,5546)" to determine the P-value. P-value = 0.0424 Decision: Since the P-value (0.0424) is less than the significance level (0.05), hence we have to reject the null hypothesis. Conclusion: From the above test we have sufficient evidence in the favour of the claim the return on the Fortune 500 portfolio is different from 0. Use a two-tailed test. 2) Degree of freedom = n - 1 Degree of freedom = 5547 - 1 Degree of freedom = 5546 Determine the critical value for tα2 using the excel formula, "=T.INV.2T(0.10,5546)": tα2=1.64512842≈1.645C.I=x¯±tα/2×sn=0.0213±1.645×0.78325547=0.0213±1.645×0.010515831=0.0213±0.017298542=0.004, 0.0386 90% confidence interval to estimate the portfolio average return is C.I = (0.004, 0.0386). Since 90% confidence interval to estimate the portfolio average return does not contains 0, hence we can conclude that the return on the Fortune 500 portfolio is different from 0. 3) We can reject the null hypothesis at conventional significance levels of 0.05 and 0.10.