Question

A mortgage service company processes a large volume of transactions every day. Because many of the transactions involve depositing funds, it is important for the company to complete processing and not leave the unprocessed items for the following day. The operations manager has a target that processing will be complete in 96% of all workdays. One of her assistant managers has been using an Excel data file where he has created a variable named “AllDone”. For the last 212 days, he has been entering a value of 1 for this variable when complete processing was achieved and 0 when unprocessed items were left for the next day. At the end of the 212^th day there were 18 zero entries under the AllDone variable and the rest were all ones. After a preliminary analysis of the data, the operations manager has concluded that “we are running short of our target and we need to step up!” At the 95% confidence level do you agree with the manager’s conclusion? Does your conclusion change at the 99% confidence level? Please show the necessary steps and interpret your results in each case.                       

Answer 1

Result:

A mortgage service company processes a large volume of transactions every day. Because many of the transactions involve depositing funds, it is important for the company to complete processing and not leave the unprocessed items for the following day. The operations manager has a target that processing will be complete in 96% of all workdays. One of her assistant managers has been using an Excel data file where he has created a variable named “AllDone”. For the last 212 days, he has been entering a value of 1 for this variable when complete processing was achieved and 0 when unprocessed items were left for the next day. At the end of the 212^th day there were 18 zero entries under the AllDone variable and the rest were all ones. After a preliminary analysis of the data, the operations manager has concluded that “we are running short of our target and we need to step up!” At the 95% confidence level do you agree with the manager’s conclusion?.    

n=212, x=212-18 = 194

p=x/n= 0.9151

Z value for 95% = 1.96

=( 0.8776, 0.9526)

95% confidence interval = (0.8776, 0.9526)

96% ( proportion of 0.96 ) not falls in the 95% CI for proportion. At the 95% confidence level we do not agree with the manager’s conclusion.

Does your conclusion change at the 99% confidence level? Please show the necessary steps and interpret your results in each case

Z value for 99% = 2.576

=( 0.8658, 0.9644)

99% confidence interval =( 0.8658, 0.9644)

96% ( proportion of 0.96 ) falls inside the 99% CI for proportion. At the 99% confidence level we do agree with the manager’s conclusion.