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Today, poles used for pole-vaulting are usually made of fiberglass and carbon fiber. A sporting goods company has developed a pole made from a new composite material and they believe that using this pole will allow vaulters to reach greater heights. They plan to conduct a study involving a sample of $30$ experienced pole-vaulters.

Each pole-vaulter will be given $5$ attempts to vault with a traditional pole made of fiberglass and carbon fiber, and their highest vault will be recorded. At a different time, each pole-vaulter will also be given $5$ attempts to vault with a pole made of the new material and their highest vault will be recorded. Which pole is used first will be randomly determined.

For each pole-vaulter, researchers will also record the difference between their highest vault using the new pole and their highest vault using the traditional pole (New – Traditional).

After verifying that the necessary conditions are satisfied, researchers plan to conduct a test.

What are the appropriate hypotheses?

A

${ H }_{ 0 }: { \mu }_{ traditional } = { \mu }_{ new }$
${ H }_{ a }: { \mu }_{ traditional } < { \mu }_{ new }$

B

${ H }_{ 0 }: { \mu }_{ traditional } = { \mu }_{ new }$
${ H }_{ a }: { \mu }_{ traditional } \neq { \mu }_{ new }$

C

${ H }_{ 0 }: { \mu }_{ difference } = 0$
${ H }_{ a }: { \mu }_{ difference } < 0$

D

${ H }_{ 0 }: { \mu }_{ difference } = 0$
${ H }_{ a }: { \mu }_{ difference } \neq 0$

E

${ H }_{ 0 }: { \mu }_{ difference } = 0$
${H }_{ a }: { \mu }_{ difference } > 0$

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