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: 9.1, 6.4, 8.0, 5.5, 8.9, 7.3, 7.4, 7.3, 7.8, 6.1, 8.6, 8.2,
8.3, 7.5, 8.7.
(a) Using the fact that x¯x¯ = 7.7 and
s = 1.095, 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)NoYes , one of the endpoints of the 95% confidence interval is above 8 seconds.
Solution:
We are given that: sample of 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: 9.1, 6.4, 8.0, 5.5, 8.9, 7.3, 7.4, 7.3, 7.8, 6.1, 8.6, 8.2, 8.3, 7.5, 8.7.
Part a) Given: Sample mean =
Sample standard deviation = s = 1.095
We have to find the 95% confidence interval for the population mean alert time, μ, for the new panel.
Formula:
where
Find tc value for c = 95% confidence level.
df = n - 1 = 15 - 1 = 14
Two tailed area= 1 - c = 1 - 0.95 =0.05
Look in t table for df = 14 and two tailed area = 0.05 and find t critical value.
Thus from t table , we get: tc = 2.145
Thus
Thus
The 95 percent confidence interval is from 7.094 seconds to 8.306 seconds.
Part (b) Can we be 95 percent confident that μ is less than 8 seconds?
No.
Since one of the endpoints of the 95% confidence interval is above 8 seconds.
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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