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Is LeBron James a more consistent scorer at home than on the road? During the 2008-2009 regular season at home, he has a mean of 25.35 points, with a standard deviation of 7.94 points in 40 games; while on the road, he had a mean of 31.46 points, with a standard deviation of 8.63 in 41 games.
a)Is 7.94 LeBron’s observed standard deviation at home or his true standard deviation at home? Explain.
b)State the hypotheses you would use to test if LeBron is more consistent at home.
c)Calculate the difference in standard deviations (road-home) and use this as the test statistic.
d)Describe how to simulate the distribution of the test statistic, assuming that LeBron is equally consistent at home and on the road.
e)Here are the results of 100 trials of the simulation. Describe what information is provided by the dotplot.
f)Based on the results of the simulation, estimate and interpret the p-value.
g)Based on the p-value, make an appropriate conclusion.
h)If your conclusion is in error, which type of error did you make? Explain.
