The mean throwing distance of a football for a 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 = 0.01. Assume the
The mean throwing distance of a football for a 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 = 0.01.
Assume the throw distances for footballs are normal. First, determine what type of test this is, set up the
hypothesis test, find the p-value, sketch the graph, and state your conclusion.
a. First, this is a test of a single population mean.
b. Null and alternative hypotheses:
c. Distribution of the test:
d. Graph:
e. Test statistic:
f. p-value:
g. Decision:
h. Conclusion:
i. Construct 95% Confidence Interval for the mean.
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