the same time. They are aided by video display panels that track the aircraft in t aths are about to converge. The display panel currently in use has a mean "alert sing between the instant when two aircraft enter into a collision course and when ording to Ralph Rudd, a supervisor of air traffic controllers at the Greater Cincinna I has been developed that uses artificial intelligence to project a plane's current f affic controllers with an earlier warning that a collision ic lilkolu It

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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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 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 Ralph Rudd, 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," µ, for the new panel is less than 8 seconds. In order to test the new panel, 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: 7.9, 8.6,
8.0, 9.2, 7.4, 7.4, 8.8, 7.5, 6.6, 8.0, 9.1, 5.5, 7.3, 8.9, 5.7.
(1) Using the fact that
= 7.8 and s= 1.170, find a 95 percent confidence interval for the population mean alert time, µ, for the new panel. (Round your answers
to 3 decimal places.)
%3D
The 95 percent confidence interval is from
to
(2) Can we be 95 percent confident that u is less than 8 seconds?
one of the endpoints of the 95% confidence interval is above 8 seconds.
Transcribed Image Text: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 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 Ralph Rudd, 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," µ, for the new panel is less than 8 seconds. In order to test the new panel, 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: 7.9, 8.6, 8.0, 9.2, 7.4, 7.4, 8.8, 7.5, 6.6, 8.0, 9.1, 5.5, 7.3, 8.9, 5.7. (1) Using the fact that = 7.8 and s= 1.170, find a 95 percent confidence interval for the population mean alert time, µ, for the new panel. (Round your answers to 3 decimal places.) %3D The 95 percent confidence interval is from to (2) Can we be 95 percent confident that u is less than 8 seconds? one of the endpoints of the 95% confidence interval is above 8 seconds.
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