Bank manager Justin Goodson has a developed a new customer complaint system to reduce the time customers spend waiting for teller services during peak hours. Waiting time used to be an average of 9 minutes. With his new method he is hoping to reach his goal of a waiting time of less than 5 minutes on average. A random sample of 105 customer customers gave a mean waiting time of 4.5 minutes and a standard deviation of 1.7 minutes. Does the evidence provide support that Justin’s new method achieved his goal of a waiting time of less than 5 minutes on average? Test at the .05 level of significance. (Z-table is at end of test.)

Identify the critical regions, clearly showing the appropriate critical value(s) and where the acceptance and rejection regions. You can either identify the regions verbally, or you can show them graphically.

Calculate the appropriate test statistic.

What decision did you make for this problem? Accepting or rejecting the null hypothesis? Interpret the decision in the context of the problem.

Calculate the p-value for this problem. Show your work.

State the Type I error in the context of the problem. What is the probability of a Type I error.