In 2003, Major League Baseball took steps to speed up the paly of baseball games in order to maintain fan interest. In a sample of 94 games in 2002, 36 finished in less than 3 hours. A similar survey in 2003 of 79 games found that 40 finished in less than 3 hours. When testing the hypothesis (at the 5% level of significance) a higher percentage of games finished in less than 3 hours in 2003, what is the test statistic? (please round your answer to 2 decimal places)

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In 2003, Major League Baseball took steps to speed up the paly of baseball games in order to maintain fan interest. In a sample of 94 games in 2002, 36 finished in less than 3 hours. A similar survey in 2003 of 79 games found that 40 finished in less than 3 hours. When testing the hypothesis (at the 5% level of significance) a higher percentage of games finished in less than 3 hours in 2003, what is the test statistic? (please round your answer to 2 decimal places)

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Step 1

For 2002 :

Sample size is N1=94N_1= 94 , Number of games in which finished in less than 3 hours  is X1=36X_1 = 36

sample proportion = p^1=X1N1=3694=0.383\hat p_1 = \frac{X_1}{N_1} = \frac{ 36}{ 94} = 0.383

 

 For 2003 :, we have that the

Sample size is N2=79N_2 = 79, Number of games in which finished in less than 3 hours is X2=40X_2 = 40

sample proportion = p^2=X2N2=4079=0.5063\hat p_2 = \frac{X_2}{N_2} = \frac{ 40}{ 79} = 0.5063

Now,  the pooled proportion is :

pˉ=X1+X2N1+N2=36+4094+79=0.4393\bar p = \displaystyle \frac{ X_1+X_2}{N_1+N_2}= \displaystyle \frac{ 36 + 40}{ 94+79} = 0.4393

 

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