Question

Credit card companies lose money on cardholders who fail to pay their minimum payments. They use a variety of methods to encourage their delinquent cardholders to pay their credit card balances, such as letters, phone calls and eventually the hiring of a collection agency. To justify the cost of using the collection agency, the agency must collect an average of at least $200 per customer. After a trial period during which the agency attempted to collect from a random sample of 100 delinquent cardholders, the 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75). Given this, what recommendation(s) would you make to the credit card company about using the collection agency

Answer 1

Answer with  explanation:

A x% confidence interval interprets that a person can be x% confident thatthe true mean lies in it.

Here, Credit card companies is using the collection agency to justify the cost of , the agency must collect an average of at least $200 per customer.

i.e. $H_0:\mu \geq200,\ \ \ H_a:\mu$

The 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75) .

I recommend that we can be 90% sure that the true mean collected amount  lies in ($190.25, $250.75).

Also, $200 lies in it such that it is more far from $250.75 than $190.25, that means there are large chances of having an average is at least $200 per customer.