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Win/Loss and With/Without Joe:

Author:
January 18th, 2023

Win/Loss and With/Without Joe: Joe playsbasketball for the Wildcats and missed some of the season due to aninjury. The win/loss record with and without Joe is summarized inthe contingency table below.

Observed Frequencies:Oi‘s

Wins Losses Totals
WithJoe   15     7     22  
Without Joe   6     12     18  
Totals   21     19     40  

The Test: Test for a significant dependentrelationship between the outcome of the game (win/lose) and whetheror not Joe played. Conduct this test at the 0.05 significancelevel.

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

H0: The outcome of the game and whether ornot Joe plays are dependent variables.

H0: The outcome of the game and whether ornot Joe plays are independentvariables.     

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

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

χ2 =  (c) USE SOFTWARE to get the P-value of the teststatistic. Round to 4 decimal places unless your softwareautomatically rounds to 3 decimal places.P-value =  (d) What is the conclusion regarding the null hypothesis?

reject H0

fail to rejectH0    

(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 dependentupon whether or not Joe played.    

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

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

Answer:

( a ) the null hypothesis for this test is

H0: The outcome of the game and whether ornot Joe plays are independent variables.  

( b ) The value of the test statistic is

( c )  P-value of thetest statistic :

with chi square = 4.821 ,df = 1

P-value = 0.02811503

~ 0.0281

( d ) conclusion :

p value < l.o.s

0.0281 < 0.05

reject H0

( e )

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

0.02811503
 
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