I don’t understand in this example how they come to the conclusion that we cannot reject the null hypothesis that alpha=0. Can someone please explain to me how they arrived to that conclusion? Thank you.
T-stat (in this case 0.4036) < 1.96 (for a 5% level of significance) ; hence we cannot reject the hypothesis that alpha=0
Thank you - can you explain why the absolute value of t-stat must be less than t-critical in order to accept versus having the t-stat fall between (+) and (-) t critical. Using example above 0.4036 falls between -1.96 and 1.96. I remember the latter from Level 1.
You pretty much answered your own question rr1102, .4036 falls between the critical value range (between -1.96 and 1.96). If it was, let’s say, -.4036, then you could say -.4036 > -1.96, hence fail to reject null. either way, the bottom line when it comes to a two-tailed hypothesis (such as this one) is that the absolute value must be less than t-critical. rr1102 Wrote: ------------------------------------------------------- > Thank you - can you explain why the absolute value > of t-stat must be less than t-critical in order to > accept versus having the t-stat fall between (+) > and (-) t critical. Using example above 0.4036 > falls between -1.96 and 1.96. I remember the > latter from Level 1.
Here’s an intuitive way to understand t-stats. Think of them as a measure of “Distance” from your null. Your test statistic is a random variable. Assume that your null is true (i.e. that alpha = 0). If you were to take random draws from your test statistic’s distribution, you’d see a lot of values close to “0”, a fair number that are 0.5 away on either side, fewer that wwere greater than 1.0 away, and so on. If you have a fairly large “n”, you can treat the t-stat like a z-stat. So, even by chance, you’ll see t-stats outside of 1 (i.e > 1 or < -1) about 1/3 of the time (remember, about 2/3 of the obs will fall within +/- 1 std deviation of zero for a normal distribution). However, by chance, you’ll only see about 5% of your observations more than 1.96 std deviations from zero. So, in this case, if the null hypothesis is true, you’d see t-statistics of greater than 1.96 or less than -1.96 only 5% of the time (hence the p-value of 0.05). THe p-va;lue actually means "the probability of observing a t-statistic of greater than the value observed BY CHANCE and ASSUMING THAT THE NULL HYPOTHESIS IS TRUE) Hope this helps. It took me a while before I got a feel for hypothesis testing. But once I realized that it was measuring “distance from the null”, it became much clearer.