Question

Win/Loss and With/Without Joe: Joe plays basketball for the Wildcats and missed some of the season due to an injury. The win/loss record with and without Joe is summarized in the contingency table below.

Observed Frequencies: O_i's

	Wins	Losses	Totals
With Joe	15	9	24
Without Joe	6	10	16
Totals	21	19	40

The Test: Test for a significant dependent relationship between the outcome of the game (win/lose) and whether or not Joe played. Conduct this test at the 0.01 significance level.

(a) What is the null hypothesis for this test?

H₀: The probability of winning is dependent upon whether or not Joe plays.

H₀: The outcome of the game and whether or not Joe plays are dependent variables.     

H₀: The outcome of the game and whether or not Joe plays are independent variables.

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ<sup>2= ?

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value = ?

(d) What is the conclusion regarding the null hypothesis?</sup>

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that Joe causes the team to do better.

The evidence suggests that the outcome of the game is dependent upon whether or not Joe played.    

There is not enough evidence to conclude that the outcome of the game is dependent upon whether or not Joe played.

We have proven that the outcome of the game is independent of whether or not Joe played.

Answer 1

The statistic software output for this problem is:

(a)

H₀: The outcome of the game and whether or not Joe plays are independent variables.

Test statistics = 2.406

P-value = 0.1209

fail to reject H₀   

There is not enough evidence to conclude that the outcome of the game is dependent upon whether or not Joe played.