1. [10]A federal agency wishes to assess the effectiveness of a new air traffic control display panel. The mean time required for air traffic controllers to stabilize an air traffic emergency in which two aircrafts have been assigned to the same air space is known to be roughly equal to 18 seconds when the current display panel is used.

To test the new display panel, 36 air traffic controllers are randomly selected, and each is trained to use the new panel to stabilize a simulated air traffic emergency. The mean of the 36 stabilization times is 14.5 seconds with a standard deviation of 3.6 seconds.

1. Find a 98% confidence interval for the true mean time required to stabilize an emergency situation using the new display panel.

2. Based on your findings in part a, do you think the new panel has a lower average stabilization time than the 18 seconds for the current display panel? Explain.

3. The federal agency would like to have a 98% confidence interval within +/- 0.5 seconds. What sample size is needed? (Assume the standard deviation remains 3.6 seconds.)