# Relationship Between P-Value and Confidence Interval in Hypothesis Testing

confidence intervalhypothesis testingp-value

Following from this question on the difference between confidence intervals and hypothesis testing, I would love to have a simple example to better understand the the relationship between confidence intervals and p-values.

For example, if I have $r=.8768 (n=300)$, then it is significant at $0.05$.

The confidence interval is (lower) $0.847729 < (r) 0.8768 < 0.900619$ (higher).

This is against 0 (i.e. no relationship).

• How does it rate with the confidence level testing?
• What do I look for?

The p-value relates to a test against the null hypothesis, usually that the parameter value is zero (no relationship). The wider the confidence interval on a parameter estimate is, the closer one of its extreme points will be to zero, and a p-value of 0.05 means that the 95% confidence interval just touches zero. In fact for a p-value $p$ of a parameter estimate, the $(1-p)$ level confidence interval just touches zero.