1
$\begingroup$

I have a model: $$Y=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3X_3+\beta_4x_4$$ and I want to test these two hypotheses: $$H_0: \beta_1>-3 \qquad H_a: \beta_1<-3$$
So if I conduct a one-sided test at the $\alpha=1\%$ significance level, the value of the $t$ statistic is over $4$. For reference, the critical value of the test statistic is $-2.326$.

I'm struggling to find the intuition for rejecting or accepting the $H_0$. The $p$ value seems to suggest reject, which I don't think the data shows.

$x ̅=-2.186$

$SE=0.2$

$(-2.186--3)/0.2=4.07$

So the critical value is $-2.326$ and the test statistic is $4.07$.

I think I reject below this, and so I would fail to reject the null hypothesis. But if the $p value$ is $0.000024$, shouldn't that mean the null hypothesis is rejected?

enter image description here

$\endgroup$
10
  • 4
    $\begingroup$ Could you elaborate a little on how you find a p-value of "almost 1" for a t statistic of "over 4"? Exactly which statistic is that, anyway? The one reported by software or one computed from your null hypothesis (which will be very different)? $\endgroup$
    – whuber
    Nov 29, 2021 at 21:57
  • $\begingroup$ I would double check whether the critical value for your t-statistic is indeed 2.326, but not, say -2.326 (and you reject $H_0$ for any t-statistic lower than the critical value). $\endgroup$
    – B.Liu
    Nov 29, 2021 at 22:03
  • $\begingroup$ Sorry, I'm using R and I have got it the wrong way around. it should be 0.000024 $\endgroup$
    – user8000
    Nov 29, 2021 at 22:07
  • 2
    $\begingroup$ My guess is that you are getting tripped up by confusing the default t-stat and p-value that come from the regression (corresponding to a two-sided null that $\beta_1=0$ against $\beta_1 \ne 0$ with the ones from your one-sided test that $\beta_1 \ge -3$ against $\beta_1 < -3$. Editing your question with the commands and output would be helpful if you want a good answer. $\endgroup$
    – dimitriy
    Nov 29, 2021 at 22:47
  • 2
    $\begingroup$ That's a truly strange drawing, because it appears to place $-2.326$ at the same distance from $0$ as $4.07.$ And what does "x" represent? The main point here is that the t-statistic you need to use is $(\hat\beta_1 - (-3)) / \operatorname{se}(\hat\beta_1),$ which will not be the t-statistic reported by the software. $\endgroup$
    – whuber
    Nov 30, 2021 at 18:20

1 Answer 1

0
$\begingroup$

You are miscalculating the p-value. If your $H_a$ is $\beta < -3$ the p-value is the area from $-\infty$ to 4.07, or 1 - 0.000024 = 0,999976.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.