Q.4 - The Practice of Statistics for AP

Question

A significance test allows you to reject a null hypothesis $H_0$ in favor of an alternative $H_a$ at the $5\%$ significance level. What can you say about significance at the $1\%$ level? 

(a) $H_0$ can be rejected at the $1\%$ significance level. 

(b) There is insufficient evidence to reject $H_0$ at the $1\%$ significance level. 

c) There is sufficient evidence to accept $H_0$ at the $1\%$ significance level. 

(d) Ha can be rejected at the $1\%$ significance level. 

(e) The answer can’t be determined from the information given 

Step-by-Step Solution

Answer

The correct answer is (E) The answer can’t be determined from the information given.

Step 1: Given Information

You reject the null hypothesis $H_0$ if and only if the $P$-value is less than the significance level.

Step 2: Explanation

At the $5\%$ significance level the null hypothesis was rejected:

$P<0.05=5\%$

We then do not know if the P-value $P$ is less than $1\%$ or not, thus answer (e) is correct.