A sports commentator believes that a particular basketball player is just awful in road games but relatively effective at home. To test this claim, the commentator takes a random sample of 36 road games and 49 home games and collects the player's scoring output in each game. He finds that in the 49 home games, the player averaged 12.3 points and his scoring output had a standard deviation of 2.6 points. Alternatively, in the 36 road games, the player averaged 8.9 points with a standard deviation of 5.6 points.
a. Specify the competing hypotheses to determine if the player has a higher scoring average in home games.
b. Calculate the value of the test statistic and the critical value at a 1% significance level. There is no reason to assume that the population variance of scoring output is equal for home and road games.
c. Does the evidence support the commentator's claim at the 1% significance level?