63 monthly stock returns for a fund between 1997 and 2002 are regressed against the market return, measured by the Wilshire 5000, and two dummy variables. The fund changed managers on January 2, 2000. Dummy variable one is equal to 1 if the return is from a month between 2000 and 2002. Dummy variable number two is equal to 1 if the return is from the second half of the year. There are 36 observations when dummy variable one equals 0, half of which are when dummy variable two also equals 0. The following are the estimated coefficient values and standard errors of the coefficients. ©Finstructor. All Rights Reserved Coefficient Value Standard error Market 1.43000 0.319000 Dummy 1 0.00162 0.000675 Dummy 2 0.00132 0.000733 What is the p-value for a test of the hypothesis that performance in the second half of the year is different than performance in the first half of the year? A) Between 0.01 and 0.05. B) Between 0.05 and
H0: Coefficient for Dummy 2 is equal to zero vs. Ha: it’s not equal to zero.
Start by calculating the t-statatistic for Dummy 2, which is 0.00132 / 0.000733 = 1.80.
Then, check the t-distribution table for two-tailed, 59 df (=n-k-1, where n=63; k=3). The table doesn’t list 59 df, but we can just use 60 df, which is a close-enough approximation. The table shows that the t-stat at 0.10 level of significance is 1.671 and 2.000 at 0.05 level of significance.
Since our t-stat 1.80 falls between these two values, the p-value (i.e., the smallest level of significance at which the null can be rejected) should be between 0.05 and 0.10.