Confidence Intervals for the Difference of Two Proportions

AP Statistics· difficulty 3/5

Constructing a two-sample z-interval for p₁ - p₂.

Why do we use unpooled SE for the CI but pooled SE for the test?

A
$The test assumes p₁ = p₂ under H₀, so we pool; the CI does not assume equality.$
check_circle
B
$Pooled SE is always larger and more accurate.$
C
$It's an arbitrary convention without theoretical basis.$
D
$The CI requires more conservative estimates, so unpooled.$

Explanation

Under H₀ (p₁ = p₂), pooling gives a better estimate of the common proportion. CIs do not assume the proportions are equal.

Want 10 more like this — adaptive to your weak spots?

Related questions