1.Air traffic controllers have the crucial task of ensuring that aircraft don't collide. 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 flight 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 a supervisor of air traffic controllers at the Greater Cincinnati International Airport, a new display panel has been developed that uses artificial intelligence to project a plane's current flight path into the future. This new panel provides air traffic controllers with an earlier warning that a collision is likely. It is hoped that the mean "alert time," , for the new panel is less than eight seconds.

a.Formulate the null hypothesis Ho and the alternative hypothesis Ha that would be used to attempt to provide evidence that is less than eight seconds.

b.Discuss the meaning of a Type I error and a Type II error in this situation.

c.The mean and the standard deviation of the sample of 15 alert times are 7.4 and 1.0261, respectively. Test Ho versus Ha by setting equal to 0.05 and using a critical value. Assume that the population of all alert times using the new display panel is approximately normally distributed.

d.Interpret the p-value of 0.02 for the test.