A bank branch located in the commercial district of a large city has developed an improved process for serving customers from 1:00 pm to 3:00 pm, which is the peak lunch period. We define the service time as the time that elapses from the time that the customer places their card inside the ATM machine until the machine prints their transaction. Let X be the service time in minutes for all customers who use the ATM machine during the peak lunch period. The objective of the improved process is to reduce the mean waiting time of all customers to less than 2.5 minutes. A random sample of 42 customers who use the ATM machine during the peak lunch period was selected. The sample measurements x are given below. At the 5% level of significance, is there enough evidence in the sample to conclude that the objective of the improved process has been met?

  

2.03 2.43 2.72 2.08 2.51 1.72 1.99 3.32 1.96 2.25 2.24 1.64 2.10 1.75 2.63 2.64 1.98 3.42 2.07 2.62 2.15 2.19 3.42 2.76 2.15 1.57 1.82 226 2.32 2.68 2.09 2.07 2.06 2.53 2.74 3.45 3.16 1.95 1.87 3.17 2.21 2.19 One-Sample Statistics N. Mean Std. Deviation Std. Error Mean 42 2.355 0.50174 0.07742 One-Sample Test Test Value = 2.5 95% Confidence Interval of the Difference df Sig. (2-tailed) Mean Difference Lower Upper 0.068 -0.145 0.301 0.011