7.2

7.5

8

6.8

7.2

8.4

5.3

7.3

7.6

7.1

9.4

6.4

7.9

6.2

8.7

Air trafc controllers have the crucial task of ensuring that aircraft don't collide. To do this. they must quickly discern when two planes are about to enter the same air space at the same time. They are aided by video display panels that track the aircraft in their sector and alert the controller when two ight paths are about to converge. The display panel currently in use has a mean \"alert time" of 15 seconds. (The alert time is the time elapsing between the instant when two aircraft enter into a collision course and when a controller initiates a call to reroute the planes.) According to Ratph Rudd, a supervisor of air trafc controllers at the Greater Cincinnati International Airport, a new display panel has been developed m that uses articial intelligence to project a plane's current ight path into the future. This new panel provides air trafc controllers with an earlier warning that a collision is likely. It is hoped that the mean \"aiert time,\" ti, for the new panel is less than 8 seconds. In order to test the new panel, 15 randomly selected air trafc controllers are trained to use the panel and their alert times for a simulated collision course are recorded. The sample alert times (in seconds) are: 7.2, 7.5, 8.0, 6.8, 7.2, 8.4, 5.3, 7.3, 7.6, 7.1, 9.4, 6.4, 7.9, 6.2, 8.7. Using the facts that the sample mean and sample standard deviation are 7.4 and 1.026. respectively, (1) Find a 95 percent condence interval for the population mean alert time. it, for the new panel. Assume normality. (2) Can we be 95 percent condent that ,u is less than 8 seconds? Explain. 1% AlertTimes