Question

The P-value for a hypothesis test is 0.06. For each of the following significance levels, decide whether the null hypothesis should be rejected.

a. $\alpha =0.05$

b. $\alpha =0.10$

c.$\alpha =0.06$

Short answer

For given value of $P=0.06$, null hypothesis should be as follows :-

(a) $\alpha =0.05$:- Not rejected

(b) $\alpha =0.10$:- Rejected

(c) $\alpha =0.06$:- Rejected

Step-by-step solution

Part (a) Step 1. Given information

Value of$\alpha =0.05$

Part (a) Step 2. Explanation

Here null hypothesis should not be rejected because $P=0.06>\alpha =0.05$

Part (b) Step 1. Given information

Value of$\alpha =0.10$

Part (b) Step 2. Explanation

Here null hypothesis should be rejected because$P=0.06<\alpha =0.10$

Part (c) Step 1. Given information

Value of$\alpha =0.06$

Part (c) Step 2. Explanation

Here null hypothesis should be rejected because$P=0.06=\alpha$.