 # One tailed or two tailed

Why is one tailed test p value is explained in the following problem? Since we test coefficient of dummy is different from 0, I thought it is two tailed test Seventy-two 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. 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 the new manager outperformed the old manager? A) Between 0.05 and 0.10. B) Lower than 0.01. C) Between 0.01 and 0.05. D) Greater than 0.10. Your answer: D was incorrect. The correct answer was B) Lower than 0.01. Dummy variable one measures the effect on performance of the change in managers. The t-statistic is equal to 0.00162 / 0.000675 = 2.400, which is higher than the t-value (with 72 - 3 - 1 = 68 degrees of freedom) of approximately 2.39 for a p-value of between 0.01 and 0.005 for a 1 tailed test.

It isn’t a one tailed test chinni. It is just saying that you can reject the null at 1% and even a little bit lower. Since your t-stat is greater than your t-critical at the 1% level you know that p-value must be smaller than 0.01.