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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 seconds2.
Based on this data, what is the 95% confidence interval (C.I.) around the mean stop time during a weekend day?
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.
For 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.