EGR 252 Ch. 9 Lecture1 JMB th edition Slide 3 Example A traffic engineer is concerned about the delays at an intersection near a local school. The intersection is equipped with a fully actuated (“demand”) traffic light and there have been complaints that traffic on the main street is subject to unacceptable delays. To develop a benchmark, the traffic engineer randomly samples 25 stop times (in seconds) on a weekend day. The average of these times is found to be 13.2 seconds, and the variance is known to be 4 seconds 2. Based on this data, what is the 95% confidence interval (C.I.) around the mean stop time during a weekend day?
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
ExampleA traffic engineer is concerned about the delays at an intersection near a local school. The intersection is equipped with a fully actuated (“demand”) traffic light and there have been complaints that traffic on the main street is subject to unacceptable delays.
To develop a benchmark, the traffic engineer randomly samples 25 stop times (in seconds) on a weekend day. The average of these times is found to be 13.2 seconds, and the variance is known to be 4 seconds2.
Based on this data, what is the 95% confidence interval (C.I.) around the mean stop time during a weekend day?
What if σ 2 is unknown? For example, what if the traffic engineer doesn’t
know the variance of this population?
1. If n is sufficiently large (n > 30), then the large sample confidence interval is calculated by using the sample standard deviation in place of sigma:
2. If σ 2 is unknown and n is not “large”, we must use the t-statistic.
Recall Our ExampleA traffic engineer is concerned about the delays at an intersection near a local school. The intersection is equipped with a fully actuated (“demand”) traffic light and there have been complaints that traffic on the main street is subject to unacceptable delays.
To develop a benchmark, the traffic engineer randomly samples 25 stop times (in seconds) on a weekend day. The average of these times is found to be 13.2 seconds, and the sample variance, s2, is found to be 4 seconds2.
Based on this data, what is the 95% confidence interval (C.I.) around the mean stop time during a weekend day?
A thermodynamics professor gave a physics pretest to a random sample of 15 students who enrolled in his course at a large state university. The sample mean was found to be 59.81 and the sample standard deviation was 4.94.
Find a 99% confidence interval for the mean on this pretest.
9.7: Tolerance LimitsFor a normal distribution of unknown mean μ,
and unknown standard deviation σ, tolerance limits are given by x + kswhere k is determined so that one can assert with 100(1-γ)% confidence that the given limits contain at least the proportion 1-α of the measurements.
Table A.7 (page 745) gives values of k for (1-α) = 0.9, 0.95, or 0.99 and γ = 0.05 or 0.01 for selected values of n.