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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 $0$.

A

I only.

B

III only.

C

I and II only.

D

II and III only.

E

I, II, and III.