For a spot speed study in which 100 observations were obtained, the mean speed was 52 mi/h and the standard deviation was 4.6 mi/h. What is the margin of error on the estimate of true mean speed obtained from this sample? What is a reasonable estimate of the 85th percentile speed based on the information available?
What will be an ideal response?
Using Equation 4.5,
For a 95% confidence level, usually used for speed data, the margin of error on
the estimate of true mean speed is ± 0.9 mi/h.
Based on the information available, the 85th percentile speed must be estimated
solely from the mean speed and standard deviation. From Table 4.1, it can be seen
that z = 1.00 for a confidence interval of 68.3% centered about the mean. Half of
this range (about 34.2% of the entire range) falls above the mean. The 85th
percentile speed is the value at which 85% of observations fall below; according
to the properties of the normal distribution, which is the entire range below the
mean plus 35% that falls immediately above the mean. Since z = 1.00 for the
34.2% of the entire range that falls immediately above the mean, then the 85th
percentile can be approximately estimated as (? + Z???when z = 1. Therefore, a
reasonable estimate of the 85th percentile speed is the sum of the mean and the
standard deviation; 52 + 4.6 = 56.6 mi/h.For a 95% confidence level, usually used for speed data, the margin of error on
the estimate of true mean speed is ± 0.9 mi/h.
Based on the information available, the 85th percentile speed must be estimated
solely from the mean speed and standard deviation. From Table 4.1, it can be seen
that z = 1.00 for a confidence interval of 68.3% centered about the mean. Half of
this range (about 34.2% of the entire range) falls above the mean. The 85th
percentile speed is the value at which 85% of observations fall below; according
to the properties of the normal distribution, which is the entire range below the
mean plus 35% that falls immediately above the mean. Since z = 1.00 for the
34.2% of the entire range that falls immediately above the mean, then the 85th
percentile can be approximately estimated as (? + Z?) when z = 1. Therefore, a
reasonable estimate of the 85th percentile speed is the sum of the mean and the
standard deviation; 52 + 4.6 = 56.6 mi/h.
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