Speed data collected on an urban roadway yielded a standard deviation in speeds of ±5.6 mi/h. (a) If an engineer wishes to estimate the average speed on the roadway at a 95% confidence level so that the estimate is within ±2 mi/h of the true average, how many spot speed observations should be collected? (b) If the estimate of the average must be within ±1 mi/h, what should the sample size be?
What will be an ideal response?
(a) Using Equation 4.5,
N = [(z ?)/d]2
N = [1.96(5.6) / 2]2
N = 30.1 => 31 spot speed observations
Note: z =1.96 for 95% confidence interval
(b)
For speeds within ±1 mi/h:
N = [1.96(5.6) / 1]2
N = 120.5 => 121 spot speed observations
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