# dummy variables and hypothesis testing

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. 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 0.10. C) Lower than 0.01. The correct answer was B) Between 0.05 and 0.10. ------------- how do i set up the null hypothesis?

Null: performance in second half of year is not different that first half peformance. i.e. coefficient on dummy 2 is not statistically different from zero. t= 0.00132 / 0.000733 = 1.80 5% significance level is something around 1.96 (not sure exactly for 63 observations, but that’s for very large samples) 10% significance is around 1.65 So 1.8 falls between the 10% and 5% significance levels. p-value = lowest level of signficance at which you can reject null, which can be done here at 1.8 and is somewhere between the 5% and 10% sig level.

i dont get why the null is set up like that can you explain the difference between these two tests 1. a test of the hypothesis that performance in the second half of the year is DIFFERENT FROM performance in the first half of the year? 2. a test of the hypothesis that performance in the second half of the year is NOT THE SAME as performance in the first half of the year?

nevermind. i see what u did

The hypothesis test of a dummy variable is basically attempting to see if that dummy variable has any explanatory power. For this question the dummy variable is used on returns in the second half of the yr, and it has a positive coefficient, which means that on average the returns in the second part of the year are greater than those in the first part. Just like any other independent variable, we want to test if it is statistically significant. So in this case, if it’s not statistically sig than we expect there is no difference between returns in the first half and those in the second half. On the other hand, if it is stat sig, the interpretation is that the difference between the returns in the second half and those in the first are statistically different from zero (i.e. the returns are not the same). So I think both of your hypothesis options above are basically equivalent, but the actual more common way to phrase the null for a dummy would be something like: “the difference between returns in 1H and those in 2H is zero.” Or, for dummy variable 1: “the difference between the returns under the first manager and those under the second manager is zero.” which we would easily reject given the high t-value.

doh!

thanks. cleared the air