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AP® Statistics

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Moderate

Refer to the Formula

APSTAT-DYLNGS

Which of the following represents the variance of the $z$-statistic for a test of the difference between two population proportions?

A

$\cfrac { \sigma }{ \sqrt { n } }$

B

$n(p)(1-p)$ where $p$ is the observed proportion of successes from both populations combined.

C

$\cfrac { \left( { p }_{ 1 } \right) \left( 1 -{ p }_{ 1 } \right) }{ { n }_{ 1 } } + \cfrac { \left( { p }_{ 2 } \right) \left( 1 - { p }_{ 2 } \right) }{ { n }_{ 2 } } $ where ${ p }_{ 1 }$ is the hypothesized proportion for population $1$ and ${ p }_{ 2 }$ is the hypothesized proportion for population $2$.

D

$\cfrac { \left( \hat { { p }_{ 1 } } \right) \left( 1 -\hat { { p }_{ 1 } } \right) }{ { n }_{ 1 } } + \cfrac { \left( \hat { { p }_{ 2 } } \right) \left( 1 - \hat { { p }_{ 2 } } \right) }{ { n }_{ 2 } } $ where $\hat { { p }_{ 1 } } $ is the observed proportion from population $1$ and $\hat { { p }_{ 2} }$ is the observed proportion from population $2$ .

E

$\left( p \right) \left( 1 - p \right) \left( \cfrac { 1 }{ { n }_{ 1 } } + \cfrac { 1 }{ { n }_{ 2 } } \right) $ where $p$ is the observed proportion from both populations combined.