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The realized mean monthly return on the S&P 500 in the 1990's appears to have been substantially different than the mean return in 2000's. The data indicate that assuming equal population variances is not unreasonable. u = 1990's population mean return and u = 2000's population mean return. The decision made in this 1 2 hypothesis is (assume at the 10% level):
Correct Answer: C
Pooled estimate of variance needs to be computed as follows: 2 2 2 S = [(60 - 1)(5.876) + (60 - 1)(4.986) ] / (60 + 60 - 2) = 29.694. 1/2 Now determine the value of t. t = [(0.7 - 1.8) - 0] / [29.964/60 + 29.964/60] = -1.101. We reject null if t > 1 .658 or t -1.658 (t-value: t(118, 0.05) = 1.658). The t value of -1.101 does not fit the rejection criteria. In other words we do not reject the null hypothesis and the t value is not significant at the 0.1 level.