Relationship between p-val and confidence interval

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What is the relationship between a p-value and a confidence interval?

A 95% confidence interval contains all values of a parameter, which if tested as null hypotheses, would give a P-value \(\geq 0.05\).

More often, we use the relationship between confidence intervals and p-values in an experimental setting, where we compare two quantities and the null hypothesis is that there is no difference. In this specific content, we can say that a 95% confidence interval of the treatment effect that does not overlap with zero implies a p-value of \(p < 0.05\).

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Confidence interval, P-value, Hypothesis testing

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In the context of standard A/B testing, a 95% CI that does not overlap with zero could mean a p-value of greater or equal than 0.05
In the context of standard A/B testing, a 95% CI that overlaps with zero suggests a p-value of less or equal than 0.05
A 95% confidence interval contains all values of a parameter, which if tested as null hypotheses, would give a P-value of greater or equal than 0.05
If the confidence interval includes zero, then the p-value is less or equal than 0.05
A 95% confidence interval contains all values of a parameter, which if tested as null hypotheses, would give a P-value of less or equal than 0.05

Relationship between p-val and confidence interval

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