Question: A large department chain issues its own credit card. The research director wants to find out whether the mean monthly unpaid balance is greater than $ 400. The level of significance is set at .05. A random check of 172 unpaid balances revealed the sample mean to be $ 407 and the standard deviation of the sample to be $ 38. Should the research director conclude that the population mean is greater than $ 400, or is it reasonable to assume that the difference of $ 7 is due to chance? What test did you perform to show this?