Quantitative Methods and Analysis - Essay Example

1. Problem A faster loan processing time increases the productivity of a bank and also leads to greater satisfaction. Let us take the example of a bank in which the bank manager wants to calculate the average loan processing time and establish a baseline for the same. Also his main purpose is to compare this average processing time with that of a competitor famous for quick loan processing. According to market information collected by his staff, the competitor claims its average processing time to be 6 hours (One-sample T-test, 2007).2. Methodology for testingThe financial analyst in the bank makes note of the processing times for 16 applications in the past month on a random basis.

The mean and standard deviation for this sample are calculated and compared with the competitor using t-test.#Loan Processing Time14253647586271084931041151271371412153164Mean5.6875Standard Deviation2.7010800313. Dependent and Independent variablesIn this t-test, customer satisfaction is the dependent variable and loan processing time is the independent variable.4. Hypothesis formulationBased on the available information, null and alternate hypothesis can be developed as follows:Ho: The loan processing time of the bank is 6 hours (Null hypothesis)Ha: The loan processing time of the bank is not equal to 6 hours (Alternate Hypothesis)5.

Formulation of Confidence IntervalsLet us use a 95% confidence interval i.e. 95% of the times the mean would lie within this interval. The confidence interval can be calculated as:CI = Mean +- t (at 5% alpha level and 15 degrees of freedom for right tailed test)*Standard deviation/n^.5i.e. CI = 5.6875 +- 1.753*(2.7011/16^.5)i.e. CI = (4.504, 6.871)6. Testing & Resultst statistic= (5.6875 – 6)/ (2.701/ (16) ^.5)i.e. t statistic = -.0289p-value for this t statistic value can be calculated at 95% confidence interval and degrees of freedom as 15 (16-1).

It comes out as .511 for a 1-tailed test which would be appropriate for this case.Since p-value > .05, the null hypothesis is accepted and it can be said that there is not a significant difference between the loan processing time of the bank from its competitor.7. ReferencesOne Sample T-Test. (2007). Statistical Interference and T-tests. Minitab Inc. retrieved October 19, 2011 from