The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marco’s mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a preset α = 0.05 distances for footballs are normal.   Construct the null and alternate hypothesis. What test statistic will you use? Give your reasons. Find the critical values which denote your rejection zones. Draw a diagram to demonstrate the rejection region.

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The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marco’s mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a preset α = 0.05 distances for footballs are normal.

 

  1. Construct the null and alternate hypothesis.
  2. What test statistic will you use? Give your reasons.
  3. Find the critical values which denote your rejection zones. Draw a diagram to demonstrate the rejection region.
  4. Calculate the test statistic and conduct the test. State whether you reject the hypothesis and interpret the result.
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