One Proportion Conf Interval
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School
University of South Carolina *
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Course
201
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
docx
Pages
3
Uploaded by CommodoreRamPerson981
Class Examples: Confidence Intervals for One Proportion
Please complete the following questions either by hand or typing answers into provided response locations.
When asked to use R to calculate values, or to construct a plot, copy and paste both the values or plot and the R
command you used to obtain the values or plot. Show work where appropriate.
1.
When a light turns yellow, should you stop or go through it? The article “Evaluation of Driver Behavior in
Type II Dilemma Zones at High-Speed Signalized Intersections” (
Journal of Transportation Engineer-
ing)
defines the “indecision zone” as the period when a vehicle is between 2.5 and 5.5 seconds away
from an intersection. It present observations of 710 vehicles passing through various intersections in
Vermont for which the light turned yellow in the indecision zone. These 710 vehicles can be considered
a representative example of the population. Of the 710 vehicles, 89 ran a red light.
A.
What is the parameter of interest in this situation?
B.
Calculate the sample proportion
^
p
.
C.
Check the conditions to perform a confidence interval for this situation.
D.
If you want to calculate a 90% confidence interval for
p
, calculate the appropriate value of
z
/2
to
six decimal places.
1
Class Examples: Confidence Intervals for One Proportion
E.
Using the appropriate formula, construct a 90% confidence interval for the proportion of vehicles
that will run the red light when encountering a yellow light in the indecision zone.
F.
Provide an interpretation for the interval found.
2.
An article describes a method of analyzing digital music files to determine the key in which the music is
written. How many music pieces should be sampled to specify the proportion that are correctly identi-
fied to within ±0.025 with 90% confidence? Assume we have no idea whatsoever regarding the true
value of
p
.
2
Class Examples: Confidence Intervals for One Proportion
3
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