Question

for a hypothesis test, alpha = 0.05
the computed p - value = 0.089
should $h_0$ be rejected?:
reject $h_0$
fail to reject $h_0$
what is the correct conclusion?
there is sufficient evidence to reject the null hypothesis and accept the alternative.
there is not sufficient evidence to reject the null hypothesis and accept the alternative.

Explanation:

Step1: Recall hypothesis - test rule

In a hypothesis test, if $P - value\leq\alpha$, we reject $H_0$. If $P - value>\alpha$, we fail to reject $H_0$.

Step2: Compare P - value and alpha

Given $\alpha = 0.05$ and $P - value=0.089$. Since $0.089>0.05$, we fail to reject $H_0$.

Step3: Determine conclusion

When we fail to reject $H_0$, there is not sufficient evidence to reject the null hypothesis and accept the alternative.

Answer:

Fail to Reject $H_0$
There is NOT sufficient evidence to reject the Null Hypothesis and accept the alternative.