A bank is testing a new method for getting delinquent customers to pay their past-due credit card bills. The standard way was to send a letter (costing about $0.45) asking the customer to pay. That worked 30% of the time. The bank wants to test a new method that involves sending a DVD to customers encouraging them to contact the bank and setup a payment plan. Developing and sending the video costs about $10 per customer.
What is the parameter of interest?
A) past-due credit card bills
B) proportion of customers who are delinquent in paying their credit card bill
C) proportion of customers who pay their credit card bill on time
D) proportion of delinquent customers who pay their credit card bill (i chose this one)
Identify the null and alternative hypotheses: How do I do this?
To identify the null and alternative hypotheses in this scenario, follow these steps:
Step 1: State the null hypothesis (H0):
The null hypothesis is the assumption of no difference or no effect. In this case, the null hypothesis would be that the new method of sending a DVD to customers does not have an impact on the proportion of delinquent customers who pay their credit card bill.
Null hypothesis (H0): The proportion of delinquent customers who pay their credit card bill using the new method is the same as the proportion using the standard method.
Step 2: State the alternative hypothesis (H1):
The alternative hypothesis is the hypothesis that contradicts the null hypothesis and suggests that there is a significant effect or difference. In this case, the alternative hypothesis would state that the new method has a different proportion of delinquent customers who pay their credit card bill compared to the standard method.
Alternative hypothesis (H1): The proportion of delinquent customers who pay their credit card bill using the new method is different from the proportion using the standard method.
Note: The alternative hypothesis could also be formulated as a one-sided test, stating that the new method is either more effective or less effective than the standard method. However, based on the given information, it seems that a two-sided alternative hypothesis is more appropriate, allowing for a difference in either direction.