Quantitative Methods

Many studies have confirmed that in the banking industry , the past due short term loans lasts 21 days on average with a standard deviation of 7days. The Bank of Development (BoD) wants to show that their short term loan product reduces the length of the past due days. They choose a sample of 25 customers for their experiment and give them short loans at the start of the quarter. The average length of the short term loans among the 25 people taking BoD loan was 18 days.

1. If you ran a test to determine if the short term loans reduce the length of a past due loan, what is the null hypothesis?

Using an alpha level or p-critical of 0.05, use statistics to show if there is a statistically significant difference in the average length of time with and without taking the short term loan. Show all of your work to prove this and indicate if you would reject your null hypothesis and why or why not.