Hypothesis Testing (Conceptual Problem)

[icystrike]

Homework Statement

This is not a homework problem, rather it is a conceptual question.

I am wondering if the below is an accurate illustration to explain why I reject the null hypothesis.
Such that
H_{0}: \mu=\mu_{0}
H_{a}: \mu\ne\mu_{0}

By relating the reasoning with the diagram attached.
1) \mu_{0}is not in the confidence interval
2) p-value < \alpha

Please suggest and comments :)

 

[Mandelbroth]

Homework Statement

This is not a homework problem, rather it is a conceptual question.

I am wondering if the below is an accurate illustration to explain why I reject the null hypothesis.
Such that
H_{0}: \mu=\mu_{0}
H_{a}: \mu\ne\mu_{0}

By relating the reasoning with the diagram attached.
1) \mu_{0}is not in the confidence interval
2) p-value < \alpha

Please suggest and comments :)

What exactly are you asking? As I understand it, you are asking if those two reasons are adequate to reject $H_0$, in which case, it almost follows directly from the definition of the ideas of confidence intervals and significance tests that they are.
I don't think you are asking that. Would you please clarify what you are asking?