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?