Moderate# 2 Proportion z-Intervals: 2-sided Testing

APSTAT-WI1N6G

A two-sample $z$-test for proportions had the hypotheses:

$${ H }_{ 0 }:{ p }_{ 1 }-{ p }_{ 2 }=0$$

$${ H }_{ a }:{ p }_{ 1 }-{ p }_{ 2 }\neq 0$$

The test produces a $p$-value of $0.04$.

Which of the following must be TRUE?

I.A $90\%$ confidence interval for the difference in proportions will contain the value $0$.

II.A $95\%$ confidence interval for the difference in proportions will contain the value $0$.

III.A $99\%$ confidence interval for the difference in proportions will contain the value $0$.