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According to some studies, women are more likely to believe in ghosts than men. Casper wondered whether women were also more likely to report having seen a ghost than men and decided to do a study.

In Casper's random sample of $85$ women, $10$ women reported having seen a ghost at some point in their lives. In his random sample of $63$ men, only $4$ reported having seen a ghost.

Which of the following shows how to calculate the z-statistic for a test of the difference in the proportions of men and women who would report that they have seen a ghost?

A

$\dfrac { \frac { 10 }{ 85 } -\frac { 4 }{ 63 } }{ \sqrt { \left( \frac { 10 }{ 85 } \right) \left( \frac { 4 }{ 63 } \right) \left( \frac { 1 }{ 85 } +\frac { 1 }{ 63 } \right) } } $

B

$\dfrac { \frac { 10 }{ 85 } -\frac { 4 }{ 63 } }{ \sqrt { \left( \frac { 14 }{ 148 } \right) \left( \frac { 134 }{ 148 } \right) \left( \frac { 10 }{ 85 } +\frac { 4 }{ 63 } \right) } } $

C

$\dfrac { \frac { 10 }{ 85 } -\frac { 4 }{ 63 } }{ \sqrt { \left( \frac { 14 }{ 148 } \right) \left( \frac { 134 }{ 148 } \right) \left( \frac { 1 }{ 85 } +\frac { 1 }{ 63 } \right) } }$

D

$\dfrac { \frac { 4 }{ 63 } -\frac { 10 }{ 85 } }{ \sqrt { \frac { \left( \frac { 4 }{ 63 } \right) \left( \frac { 59 }{ 63 } \right) }{ 63 } +\frac { \left( \frac { 10 }{ 85 } \right) \left( \frac { 75 }{ 85 } \right) }{ 85 } } }$

E

$\dfrac { \frac { 4 }{ 63 } -\frac { 10 }{ 85 } }{ \sqrt { \frac { \left( \frac { 4 }{ 63 } \right) \left( \frac { 10 }{ 85 } \right) }{ 148 } +\frac { \left( \frac { 59 }{ 63 } \right) \left( \frac { 75 }{ 85 } \right) }{ 148 } } } $

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