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A traffic engineer wishes to determine whether cell phone use while driving causes subjects to speed.

The engineer has organized for subjects’ friends to call while they are driving on a highway and then records their speeds before, during, and after the call.

A test is performed on the following hypothesis:

$H_0: { P }_{ \text{phone} }= { P }_{ \text{no phone} }$
$H_a: { P }_{ \text{phone} } ≠ { P }_{ \text{no phone} }$

Define ${ P }_{ \text{phone} }$ as the proportion who speed while on the phone and ${ P }_{ \text{no phone} }$ as the proportion who speed while not on the phone.

If this test yields a $p$-value of $0.0782$, which of the following conclusions can be made?

A

A $90\%$ confidence interval will NOT contain $0$.

B

A $95\%$ confidence interval will NOT contain $0$.

C

A $99\%$ confidence interval will NOT contain $0$.

D

Both $90\%$ and $95\%$ confidence intervals will contain $0$.

E

A $99\%$ confidence interval will contain $0.0782$.

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