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CEE 6601 Spring 2019

Georgia Institute of Technology

School of Civil and Environmental Engineering

Homework Assignment 2 (45 points)

Due 3 p.m. Tuesday, February 5, 2019

To receive maximum credit, show all work and explain your answers. On this assignment, when I ask for a hypothesis test, “showing your work” means providing the null and alternative hypotheses, noting (or providing) the value of α, presenting the test statistic, stating (or showing on a plot) the rejection and acceptance regions, reporting the result of the test, and interpreting the result (i.e., don’t just say “reject” or “FTR” H0, but explain what that outcome means in the context of the problem).

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1.According to 2015 U.S. census data, the nationwide median family income is $62,982. We are interested in the income difference between Georgia and the nation. We randomly selected 16 counties in Georgia, shown in Table 1. Is there evidence to support the claim that the average value of median family income for counties in Georgia is different than the national level? Assuming that median income at the county level is normally-distributed, conduct the appropriate hypothesis test about the claim at the 1% significance level, and state the results in plain English. (5 points)

Table 1. 2015 Median Family Income by County

IndexCounty NameMedian Family Income

1Fulton$75,579

2Coweta$96,501

3Fayette$92,976

4Oconee$85,371

5Cobb$78,920

6Harris$74,457

7Cherokee$77,190

8Columbia$74,426

9DeKalb$60,718

10Bryan$72,118

11Glynn$62,445

12Morgan$57,724

13Gwinnett$70,767

14Forsyth$68,469

15Pickens$59,955

16Henry$70,972

2.We are interested in comparing the traffic conditions of Cities A, B, and C. Traffic data collectors are installed on major corridors to monitor real-time travel speeds. Speed data from each city are randomly sampled during 10-11 am on a certain weekday, and shown in Table 2. For problems 2a)-b), conduct the appropriate hypothesis test at the 5% significance level. (12 points)

a)Test the hypothesis that people drive at different speeds in City B than in City A, assuming the population variances are equal. (5 points)

b)Test the hypothesis that people drive at different speeds in City B than in City A, assuming the population variances are unequal. (5 points)

c)Compare your two answers. (2 points)

Table 2. 10-11AM Speed Observations (mph) on Sampled Corridors in 2 Cities

28.628.4

31.717.3

26.122.5

22.315.4

15.023.5

22.828.8

22.125.0

17.022.1

27.422.9

23.527.0

14.227.1

17.018.6

21.624.1

21.434.2

18.717.5

13.620.6

19.832.5

24.330.2

3.In the U.S., lanes in multiple corridors have been converted to high-occupancy vehicle (HOV) lanes in order to reduce congestion. Ten HOV corridors are selected to evaluate the performance of HOV lanes. Average annual peak-period speeds are collected before and after the HOV conversion, as shown in Table 3. We are interested in whether the conversion improves traffic, but because we are skeptical scientists, we also entertain the possibility that it might have made traffic worse. Conduct the appropriate hypothesis test at the 5% significance level. (5 points)

Table 3. Before-after Peak-period Speed (mph) of Sampled Corridors

Corridor IDBeforeAfter

14543

24855

35360

44047

54547

64651

74755

83844

94946

104148

4.There are five electric vehicle (EV) charging stations in the neighborhood Peter lives in. Peter thinks he uses each charging station about equally often (meaning that the distribution of his recharge visits across stations is “discrete uniform”). When Peter looks at the history of his past 100 recharging events, the number of visits to each station is shown in Table 4. Do the historical data support Peter’s supposition? Conduct the appropriate hypothesis test at the 1% significance level. (5 points)

Table 4. Number of Visits per Charging Station

Station ID12345

Number of Visits2022182614

5.We are interested in exploring whether or not vehicle ownership (the number of vehicles owned by a household) is associated with having a private parking garage. 500 households are randomly selected. Their vehicle ownership is categorized into 5 categories and parking information is categorized into two categories, shown in Table 5. Do the data suggest that vehicle ownership and private parking garage are related in the population sampled? If you see a relationship, is it consistent with your expectations? Explain. Conduct the appropriate hypothesis test about the claim at the 5% significance level. (6 points)

Table 5. Vehicle Ownership and Private Parking Garage

Number of VehiclesTotal

01234+

With Private Parking Garage2044985015227

Without Private Parking Garage40135661814273

Number of Households601791646829500

6.Many transit agencies are faced with the issue of delay, i.e. buses cannot catch up with their scheduled time. To reduce bus delay, signal prioritization for buses at signalized intersections has been implemented on two routes, A and B. The table below shows the performance of several trips on two routes. (6 points)

Table 6. Delay Time (Seconds) of Route A and B

4575

6580

6585

7085

7090

7590

80110

300110

a)Calculate the average and median values of delay time for each route. (2 points)

b)Is the performance on Route A better than Route B? Why? (2 points)

c)Is the average value a better measure of the performance than the median? Why? (2 points)

7.Jack bought a hybrid-electric car and wanted to evaluate whether or not the car indeed saves fuel. He used an OBD logger and measured his daily MPG (i.e. miles per gallon, a metric commonly used to evaluate fuel economy). He found that MPG could be derived from speed as a strictly convex function, shown in Figure 1. At the average speed, i.e. 32 mph, the function yields 13 MPG. (6 points)

a)What is the average MPG of the function? (2 points)

A.13 MPG

B.higher than 13 MPG

C.lower than 13 MPG

D.32 MPG

E.none of the above

b)If Jack drives his 13-mile commute at the average speed, i.e. 32 mph, how much fuel will he need? (2 points)

A.1 gallon

B.higher than 1 gallon

C.lower than 1 gallon

D.32 gallons

E.13 gallons

F.none of the above