3. 1000 points value: Exercise 8.19 THE AIR TRAFFIC CONTROL CASE Air traffic con

Question

3. 1000 points value: Exercise 8.19 THE AIR TRAFFIC CONTROL CASE Air traffic 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 flight paths are about to converge. The display panel currently in use has a mean "alert time" of 15 seconds. The alert me is the time elapsing between e instant when two aircraft enter intoa ollision course and when a controller initiates a oute the p es According to Rudd, a super sor a 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 ea er warning that a collision 1s likely t is hoped hat he mean alert time, or the new panel s less han 8 seconds. In order to test the new ane 15 randomly selected air traffic 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: 5.9, 9.2,8.0, 7.4,6.5, 5.7, 8.0, 9.5, 5.6, 8.6, 5.8, 6.9, 6.0, 8.7, 8.2 a Using the fact that -7.3 and S-1.353, find a 95 per ent confidence interval for the population mean a rt me or The 95 percent confidence interval is from (b) Can we be 95 percent confident that p is less than 8 seconds? e new pane. Round your answers to 3 de mal places. to , one of the endpoints of the 95% confidence interval is above 8 seconds.

Explanation / Answer

Since this is a sample of 15 alert times, we will use T-distribution to find the confidence interval.

Degrees of freedom = 15-1 = 14

= (1-0.95) /2 = 0.025

From t-distribution table, df = 14, = 0.025 , t value = 2.145

s x = Standard error = (1.3532/15) = 0.35

= X ± t(sx)
= 7.3 ± 2.145*0.35
= 7.3 ± 0.749 = 7.3, 95% CI [6.551, 8.049].

You can be 95% confident that the population mean () falls between 6.551 and 8.049.

Part 2 - The upper limit of alert time 0.049 seconds above 8 seconds. The answer is Yes.

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