Question

An NBA fan named Mark claims that there are more fouls called on his team any other team, but the commissioner says that the number of fouls called against his team are no different than any other team. Mark finds that the average number of fouls in any game in the NBA is 11.5. He takes a random sample of 34 of games involving his team and finds that there are an average of 12.2 fouls against his team, with a standard deviation of 1.6 fouls. What is the correct conclusion

Answer 1

Fouls > Average Fouls

Explanation:

Null Hypothesis [ H0 ] : Fouls = Average Fouls ie 11.5

Alternate Hypothesis [ H1 ] : Fouls > Average Fouls

t = ( x - u ) / ( s / √n )

where x = actual observed mean = 12.2 here , u = assumed population mean = 11.5 , s = sample standard deviation = 1.6 , n = sample size = 34

So, t = (12.2 - 11.5 ) / ( 1.6 / √34 ) = 0.7 / ( 1.6 / 5.83 ) = 0.7 / 0.275 = 2.55

t tabulated value for α = 5% right tailed = 1.645 , ie < calculated value 2.55 So , we reject the null hypothesis, & conclude that 'Fouls > Average Fouls'