Background Letter from Torrance Transit System to Dr. Drew.
Their Question If we only do two round-trips per survey day (362 round-trips, or 724 one-way trips), would our data meet the 95% confidence, 10% accuracy FTA criteria? If not, would there be a way of adding a few extra surveys to meet the standard?
Sampling Schemes FTA(Federal Transportation Administration) Sampling scheme: Every 2 nd day/ 3 one-way trips/ 549 one-way trips per year Torrance Transit Sampling scheme: Every 2 nd day/ 2 round trips/ 362 round trips (724 one-way trips)
Finding what to do
Things to do Read US Department Transportation Booklet for Sampling Procedure. Contact with David Banks, statistician of US Department of Transportation. Read relevant documents from Torrance Transit System.
Initial thought Correlation between the average travel mileage in Westbound & the average travel mileage in Eastbound
I got you!!
Meeting with folks in Torrance Transit System
Homework Assignment to Torrance Transit System folks Collect a sample of 13 round trips.
Var[ m ] = n -2 ( Σ i Var[ X i ] + Σ i≠j Cov[ X i, X j ]) = n -2 ( n σ 2 + nc ) = (σ 2 + c )/n = σ 2 (1 + ρ )/n
Let’s find the correlation coefficient for which the proposed sampling scheme provides information equivalent to the FTA sampling scheme. σ 2 /549 = σ 2 (1 + ρ )/ 724 ρ=.3188.
0.536 Estoy mucha triste!!
Find the sample size (n) required to meet the federally defined criteria. ρ = σ 2 /549 = σ 2 (1 + ρ )/ n σ 2 /549 = σ 2 ( )/ n n = X 549 n = 844 one-way trips or 422 round trips
Conclusion Torrance Transit System needs to make 60 more round-trips (= 422 – 362) or 120 more one-way trips (= 60 X 2).