A large bank wants to estimate the average amount of money owned by its delinquent debtors. The bank randomly samples 100 of its delinquent accounts and finds that the sample mean amount owed is $230, and the standard deviation is $90.

• Find the 95% confidence interval for the average amount of money owned by delinquent debtors
• Find the 99% confidence interval for the average amount of money owned by delinquent debtors
• Which interval (95% or 99%) is more likely to include the unknown population mean? Why?
• Test the hypothesis that the average amount of money owned by delinquent debtors is $256, against the two-sided alternative. (At the 5% level of significance).