Rejecting or Accepting Null Hypothesis

Question

The question states:

We take a sample and find a $95\%$ confidence interval for the mean of $(24.2, 28.4)$. If we are testing $H_0 : \mu = 24$ against $H_1 : \mu > 24$ at the $5\%$ level of significance

What is our conclusion?

(A) Reject $H_0$,

(B) Fail to reject $H_0$,

(C) Can’t tell

I can't really solve this... I've got:

$x_{bar} + \text{Error} = 28.4$

$x_{bar} - \text{Error}= 24.2$

$x_{bar} = 26.3$, so $\text{Error}= 2.1$

$Z_{\alpha/2} = 1.96$

So $\sigma/n^{1/2} = 1.2766$

But I dont know how to move from there...

Thank you, hope you can help.

Answer 1

Based on the confidence interval, reject $H_0$ because $24 \notin (24.2, 28.4)$ i.e the C.I. provides evidence against the null in favour of the alternative.