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A Sports Commentator Believes That a Particular Basketball Player Is

question 103

Essay

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?

Definitions:

Representatives

Elected officials in the legislative branch of government tasked with making and enacting laws, typically on behalf of a specific geographic area or constituency.

Casework

The assistance provided by members of legislative bodies to constituents dealing with governmental agencies and systems, often involving personal problems or requests.

Federal Government

The national government of a federal country, where powers are divided between the central authority and constituent units or states.

Congress

The national legislative body of the United States, consisting of two chambers: the Senate and the House of Representatives.