SOLUTION: This is not in a textbook, can you help? Two banks in the Greensboro NC area compete for credit card customers. In order to select the better bank, we want to test whether there

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Question 130994: This is not in a textbook, can you help?
Two banks in the Greensboro NC area compete for credit card customers. In order to select the better bank, we want to test whether there is a difference in the proportion of times a customer is able to reach the customer service representative in less than 2 minutes. We have called the first bank 500 times and were able to speak to the customer service rep on 455 occasions. Then we attempted to call the second bank and were able to speak to service rep 344 of 400 trials. At the 0.05 significance level is there a difference in percentages of success between these two banks?
Answer by stanbon(75887) About Me  (Show Source):
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test whether there is a difference in the proportion of times a customer is able to reach the customer service representative in less than 2 minutes. We have called the first bank 500 times and were able to speak to the customer service rep on 455 occasions. Then we attempted to call the second bank and were able to speak to service rep 344 of 400 trials. At the 0.05 significance level is there a difference in percentages of success between these two banks?
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Ho: p1 - p2 = 0
Ha: p1 - p2 is not zero
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p1-hat = 455/500 = 0.91
p2-hat = 344/400 = 0.86
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Critical value for 2-tail test and alpha=5%: +-1.96
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Test statistic:
Pooling the data you get p-bar = (455+344)/(500+400)= 0.88777
z(0.91-0.86)= (0.05/sqrt[(0.888*0.112/500 + (0.888*0.112/400)] = 2.3634..
p-value = 2*P(2.3634 -----------------
Conclusion:
Since p-value is less than 5%, reject Ho.
There is significant statistical evidence that there is
a difference between the two proportions.
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Cheers,
Stan H.
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