The manager of a department store is thinking about establishing a new billing system for the store's credit customers. She determines that the new system will be cost-effective only if the mean monthly account balance is more than $170. A random sample of 400 monthly accounts is drawn, for which the sample mean is $178. The manager knows that the accounts are approximately normally distributed with a standard deviation of $65. a) Can the manager conclude from this that the new system will be cost-effective at a 5% level of significance? [Define your parameter and show all 6 steps procedure]