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: 7.3, 9.3, 8.0,
9.4, 8.8, 6.5, 7.3, 7.0, 8.7, 9.1, 8.4, 6.1, 7.0, 7.4,
6.3.
(a) Using the fact that x¯x¯ = 7.8 and s = 1.142, find a 95 percent confidence interval for the population mean alert time, μ, for the new panel. (Round your answers to 3 decimal places.)
The 95 percent confidence interval is from to .
(b) Can we be 95 percent confident that μ
is less than 8 seconds?
(Click to select)Yes OR No , one of the endpoints of the 95% confidence interval is above 8 seconds.
a)
xbar = 7.8 , sd = 1.142 ,n= 15
df =n-1 = 14
t = 2.1447
(xbar - t * sd/sqrt(n) , xbar +t * sd/sqrt(n) )
(7.8 - 2.1447 * 1.142 /sqrt(15) , 7.8 - 2.1447 * 1.142 /sqrt(15))
= (7.168,8.432)
The 95 percent confidence interval is from (7.168,8.432)
b)
No, one of the endpoints of the 95% confidence interval is above 8 seconds.
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Air traffic controllers have the crucial task of ensuring that aircraft don't collide. To do this,...
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...
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...
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