统计学作业Assignment代写 Homework代写

Homework Assignment 2 (45 points)

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

统计学作业Assignment代写 He used an OBD logger and measured his daily MPG (i.e. miles per gallon, a metric commonly used to evaluate fuel economy).

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 统计学作业Assignment代写

Index	County Name	Median Family Income
1	Fulton	$75,579
2	Coweta	$96,501
3	Fayette	$92,976
4	Oconee	$85,371
5	Cobb	$78,920
6	Harris	$74,457
7	Cherokee	$77,190
8	Columbia	$74,426 统计学作业Assignment代写
9	DeKalb	$60,718
10	Bryan	$72,118
11	Glynn	$62,445
12	Morgan	$57,724
13	Gwinnett	$70,767
14	Forsyth	$68,469
15	Pickens	$59,955
16	Henry	$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) 统计学作业Assignment代写

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

A	B
28.6	28.4
31.7	17.3
26.1	22.5
22.3	15.4
15.0 统计学作业Assignment代写	23.5
22.8	28.8
22.1	25.0
17.0	22.1
27.4	22.9
23.5	27.0
14.2	27.1
17.0	18.6
21.6	24.1
21.4	34.2
18.7	17.5
13.6	20.6
19.8	32.5
24.3	30.2
27.7
18.6

3.In the U.S., lanes in multiple corridors have been converted to high-occupancy vehicle (HOV) lanes in order to reduce congestion. 统计学作业Assignment代写

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 ID	Before	After
1	45	43
2	48	55
3	53	60
4	40	47
5 统计学作业Assignment代写	45	47
6	46	51
7	47	55
8	38	44
9	49	46
10	41	48

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 ID	1	2	3	4	5
Number of Visits	20	22	18	26	14

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. 统计学作业Assignment代写

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) 统计学作业Assignment代写

Table 5. Vehicle Ownership and Private Parking Garage

	Number of Vehicles					Total
	0	1	2	3	4+
With Private Parking Garage	20	44	98	50	15	227
Without Private Parking Garage	40	135	66	18	14	273
Number of Households	60	179	164	68	29	500

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) 统计学作业Assignment代写

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

A	B
45	75
65	80
65	85
70	85
70	85
70	90
75	90
75	90
75	90
80	110
300	110

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) 统计学作业Assignment代写

7.Jack bought a hybrid-electric car and wanted to evaluate whether or not the car indeed saves fuel. 统计学作业Assignment代写

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

c)If Jack drives 13 miles for his commute, what is the average fuel consumption? (2 points) 统计学作业Assignment代写