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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:

Noncumulative

Pertains to dividends that, if missed by a company, are not required to be paid out to shareholders in the future.

Diluted Earnings Per Share

A calculation of earnings per share that includes potential shares from convertible securities, providing a "worst-case" scenario of earnings per share.

Basic Earnings

The amount of profit attributable to shareholders before deductions for preferred dividends, calculated on a per-share basis.

Continuing Operations

The portions of a business’s activities expected to continue for the foreseeable future, as opposed to activities that are being discontinued or phased out.