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AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 10

Lesson 9: Testing for the difference of two population proportions

Writing hypotheses for testing the difference of proportions

AP.STATS: VAR‑6 (EU), VAR‑6.H (LO), VAR‑6.H.1 (EK), VAR‑6.H.2 (EK), VAR‑6.H.3 (EK)

Researchers want to study the effectiveness of a new medication to treat depression. In a randomized experiment, 71 out of 200 people taking the medication report symptoms of depression. Of the people receiving a placebo, 92 out of 200 report symptoms of depression. The researchers want to use these results to test if the medication is working any differently than the placebo.

Let p, start subscript, 1, end subscript be the true proportion of individuals like the ones in this study who take the new medication and report symptoms of depression, and p, start subscript, 2, end subscript be the true proportion of individuals like the ones in this study who take a placebo and report symptoms of depression.

Which of the following is an appropriate set of hypotheses for their significance test?

(Choice A)
$\begin{aligned} &H_0: p_{1} = p_{2}\\ &H_\text{a}: p_{1} < p_{2} \end{aligned}$
(Choice B)
$\begin{aligned} &H_0: p_{1} = p_{2}\\ &H_\text{a}: p_{1} > p_{2} \end{aligned}$
(Choice C)
$\begin{aligned} &H_0: p_{1} = p_{2}\\ &H_\text{a}: p_{1} \neq p_{2} \end{aligned}$
(Choice D)
$\begin{aligned} &H_0: p_{1} \neq p_{2}\\ &H_\text{a}: p_{1} = p_{2} \end{aligned}$

Stuck?

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 10

Problem