State the hypotheses that can be used to determine whether t

State the hypotheses that can be used to determine whether the population proportions of delayed departures differ at these two airports.
H0: p1 - p2
Ha: p1 - p2

What is the point estimate of the proportion of flights that have delayed departures at Chicago O\'Hare (to 2 decimals)?

What is the point estimate of the proportion of flights that have delayed departures at Atlanta Hartsfield-Jackson (to 2 decimals)?

What is the p-value for the hypothesis test (to 4 decimals)?


What is your conclusion?

Solution

Formulating the hypotheses          
Ho: p1^ - p2^   =   0  
Ha: p1^ - p2^   =/=   0   [ANSWERS]

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Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 = 252/900 =    0.28   [ANSWER] for Chicago O\'hare]

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p2 = x2/n2 = 312/1200 =     0.26   [for Atlanta Hartsfeld Jackson]  

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Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.019604421      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    1.020178037      
          
As significance level =    0.05   , then the critical z is  
          
zcrit =    1.959963985      
          
Also, the p value is          
          
P =    0.307644032   [ANSWER, P VALUE  

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As P > 0.05, we FAIL TO REJECT HO.

There is no significant evidence that the population proportions of delayed departures differ at these two airports. [CONCLUSION]