Question

p - value = 0.0139
part: 3 / 5
part 4 of 5
determine whether to reject h₀.
since p select 0.10, we reject the null hypothesis h₀ at α = 0.10.
since p select 0.01, we do not reject the null hypothesis h₀ at α = 0.01.

Explanation:

Step1: Recall Hypothesis Testing Rule

In hypothesis testing, we reject \( H_0 \) if \( P\text{-value} < \alpha \), and do not reject \( H_0 \) if \( P\text{-value} \geq \alpha \).

Step2: Analyze for \( \alpha = 0.10 \)

Given \( P\text{-value} = 0.0139 \) and \( \alpha = 0.10 \). Since \( 0.0139 < 0.10 \), we reject \( H_0 \) at \( \alpha = 0.10 \).

Step3: Analyze for \( \alpha = 0.01 \)

Given \( P\text{-value} = 0.0139 \) and \( \alpha = 0.01 \). Since \( 0.0139 > 0.01 \), we do not reject \( H_0 \) at \( \alpha = 0.01 \).

Answer:

For \( \alpha = 0.10 \): reject
For \( \alpha = 0.01 \): do not reject