Problem 1) A bank is testing a new method for getting delinquent customer to pay

Question

Problem 1) A bank is testing a new method for getting delinquent customer to pay their past-due credit card bills. The standard way was to send a letter asking the customer to pay; this worked 30% of the time. They hope to improve on the rate of payment with a new method that involves emailing the customer encouraging them to contact the bank and set up a payment plan. The bank selects a random sample of delinquent customers who received the new emails, conducts a significance test, and finds the z test statistic = 2.64.

a) What are the hypotheses?

b) What is the P-value?

c) What is the conclusion of the significance test in the context of the problem? (not just “reject Ho” or “do not reject Ho”)

Explanation / Answer

a) Our null and alternative hypotheses will be:

Ho: The new method for getting delinquent customer to pay their past-duecredit card bills does not improve the rate of payment i.e. p = 0.3

H1: The new method for getting delinquent customer to pay their past-duecredit card bills improves the rate of payment i.e. p > 0.3

b) This is a right tailed test since alternative hypothesis contains the sign ">".

So,

p - value = P(z > 2.64) = 0.0041

c) Since p - value is very small, we reject the null hypothesis. Hence,

There is sufficient evidence to support that the new method for getting delinquent customer to pay their past-duecredit card bills improves the rate of payment.

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