0

So I'm trying to perform a $t$ test with sample mean $\bar{x}$ and sample variance $s^2$. I know how to do this with $H_0 = a$ and $H_a \ne a$. But now I'm given $H_0 < a$ and $H_a \ge a$. How do I modify the $t$ test formula?

PTN
  • 205

1 Answers1

1

Normally, you should use one tailed test. When $H_0 : \mu<a$, it is not strange that $t=\frac{\overline{x}-a}{\sqrt{\frac{s^2}{n}}}$ is negative. So, even when $t$ is $-500$, $H_0$ is not rejeted. However, t is larger than $t_\alpha$(not $t_{\frac{\alpha}{2}}$), it is rejected.

dyna
  • 106
  • 6
  • So I would still plug constant $a$ into the function like normal? I thought I have to like pick a value $< a$ – PTN Mar 04 '19 at 05:03
  • 1
    Yes. In fact, normally we think that $H_0:\mu=a$ and $H_1:\mu>a$. I think you say about this pattern. However, if you say about another pattern, this answer is not useful for your question. Soery. – dyna Mar 04 '19 at 05:15