A bank is trying out a new system through which it hopes to reduce its customers’ waiting time and keep them satisfied. The bank manager hopes that the new system will reduce the customers’ waiting time—from beginning till checking out—to not more than 5 minutes. The new system will reduce the waiting time to 3.5 minutes, with a standard deviation of 1.96 minutes. To verify the performance, the bank manager measures 30 customers’ waiting time using the new system and obtains mean waiting time of 4.17 minutes.

a. Use these data to test the null hypothesis at a 1%
level of significance.

b. Determine the probability that a wrong decision was made in part

a, where the new system actually provided a waiting time of 3.5 minutes as stated in the question.