How is a CI related to a hypothesis test?

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Answer

$A 95% CI for a parameter includes all null values that would NOT be rejected at α = 0.05 in a two-sided test.$
$Equivalently: if 0 is outside the 95% CI of the difference, then reject H0: no difference at α = 0.05.$
$CIs are more informative — they give you the range of plausible values, not just accept / reject.$
$Always report CIs.$

Check yourself — multiple choice

Unrelated
95% CI = values not rejected at α=0.05 in two-sided test; CI is more informative than accept/reject — report CIs
Same as p-value
Only frequentist

CI ↔ hypothesis test: 95% CI = values not rejected at α=0.05; CI more informative.

#hypothesis-testing#confidence-interval

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