# Simple Quant Q

QUick Q: If a question says use the t-test to determine if the coefficient is significantly greater than or equal to 0. Then H0: B1 >= 0 Ha B1 <= 0 Now let’s say the Critital value is -2.65 and the T stat = -3. Can you please explain the decision to reject or not. Thanks

absolute value of -3 = 3 which is > 2.65, reject Ho, stat significant

okay so there’s no real difference if we are looking to test if the coefficient is 0, >0 or <0? What if the question was: Use the t-test to determine if the coefficient is significantly less than or equal to 0. Then H0: B1 <= 0 Ha B1 >= 0 Again let’s say the Critital value is -2.65 and the T stat = -3.

btw, these s/b two tailed tests to test whether coefficient is not 0, so hypothesies would be: H0: B1 = 0 and Ha: B1 >< 0 But if we are trying to find out if the coefficient is greater than 0 then: With a t-stat of -3 then either B1-B1bar is neg or the std error is neg, and since std error cannot be neg, then B1-B1bar is neg. if we use 0 as B1bar then your B1 is negative and with a t-stat of -3 is not significant enough to reject the null.

since your given the T stat, thats all. If it didnt give it to you: say it gave you B1 = 1 and the standard error is 2 t- stat: (1 - 0)/2 = .5, since its less than critical value, accept Ho

The issue is that if you are just testing if a number is > 0, this will be a one tailed test, so the absolute value of the critical t will be less than the t for a similar test at the same significance level. Whether that t is positive or negative, I don’t remember, but I think you want a positive t for testing if the value is > 0. In practice, all that matters is the absolute value of t, since you will know whther the statistic you are testing is > or < 0.

mambovipi Wrote: ------------------------------------------------------- > QUick Q: > > If a question says use the t-test to determine if > the coefficient is significantly greater than or > equal to 0. > > Then H0: B1 >= 0 > Ha B1 <= 0 > > Now let’s say the Critital value is -2.65 and the > T stat = -3. Can you please explain the decision > to reject or not. > > Thanks Hey, just a reminder that you should never have equal sign in the alternative hypothesis.

North is correct. If you’re already given T-Crit , just use it , doesn’t matter tails or not. If not , and you have to use t tables , choose the right column . in this case you use 1-T distribution .Or halve the significance and choose the 2-T

you need to use two tailed test. F-test is one tail