To determine whether to reject or fail to reject the null hypothesis ([tex]\(H_0\)[/tex]), we need to compare the [tex]\(P\)[/tex]-value with the given level of significance ([tex]\(\alpha\)[/tex]).
Step-by-Step Solution:
1. Identify the [tex]\(P\)[/tex]-value: The [tex]\(P\)[/tex]-value provided in the problem is [tex]\(P = 0.006\)[/tex].
2. Identify the level of significance ([tex]\(\alpha\)[/tex]): The level of significance provided is [tex]\(\alpha = 0.01\)[/tex].
3. Compare the [tex]\(P\)[/tex]-value to [tex]\(\alpha\)[/tex]:
- If the [tex]\(P\)[/tex]-value is less than [tex]\(\alpha\)[/tex], we reject the null hypothesis ([tex]\(H_0\)[/tex]).
- If the [tex]\(P\)[/tex]-value is greater than or equal to [tex]\(\alpha\)[/tex], we fail to reject the null hypothesis ([tex]\(H_0\)[/tex]).
4. Perform the comparison:
- Given [tex]\(P = 0.006\)[/tex] and [tex]\(\alpha = 0.01\)[/tex],
- We see that [tex]\(0.006 < 0.01\)[/tex].
5. Decision: Since the [tex]\(P\)[/tex]-value [tex]\(0.006\)[/tex] is less than the level of significance [tex]\(\alpha = 0.01\)[/tex], we reject the null hypothesis ([tex]\(H_0\)[/tex]).
Therefore, the appropriate response is:
A. reject [tex]\(H_0\)[/tex].
