Math& 146 Exam 3-4,
Closed notes, closed book, calculator ok
Page 1 of 4
Name __________________________ Points ______/
1. While it may seem that having more electric cars on the highway is a good thing because of
the reduced consumption of gas and the reduction in carbon emissions, there is a consequence.
Highway construction and repair is paid for by gasoline taxes that are currently about $0.37 per
gallon. Since electric cars don’t use gas, but they do use the roads, then those drivers are not
contributing to the highway funds. A proposal is being debated to have people pay about 2 cents
for every mile they drive instead of paying a gas tax. The mileage can be determined by either
annual verification of miles or using electronics to relay all driving information to the
government or private agency.
To determine the public support for this new policy and the effectiveness of the data
collection system, randomly selected drivers were called. They were first asked if they thought
the new mileage fee was a good idea. There answers were expected to be yes or no.
1a. Is the data categorical or quantitative?
Circle 1: Categorical
Quantitative
1b. Because of the possibility that rural drivers may have a different opinion than urban drivers,
some of the sample was taken from rural drivers and the remaining part of the sample was taken
from urban drivers. Which type of sampling method is being described?
Circle 1: Simple Random
Stratified
Systematic
Cluster
1c. Suppose there are 4,000 drivers in one rural county in Washington numbered from 1 to
4,000. If you randomly select some of these drivers, what will be the numbers of the first three
drivers you select if you seed your calculator with 26 or you use row 40 in the table of random
numbers below.
______, _______, _______
Out of 800 people who were called, 320 said yes, it was a good idea. The rest said no, it wasn’t a
good idea.
1e. What is the sample proportion of people who think it is a good idea?
1e_________________
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Math& 146 Exam 3-4,
Closed notes, closed book, calculator ok
Page 2 of 4
1f. Make a pie chart for this data (320 out of 800 said yes). Provide a title, and then label each
slice with the data label, number and percent.
1g. Based on this data, can we conclude that a majority of people think this mileage tax is a
good idea (H0: p = 0.5, H1: p > 0.5, α = 0.05) if the p-value is 0.99?
Circle 1: Yes No
1h. During the survey, drivers were also asked if they would be willing to test the new system
on their car. Two different electronic systems, System A and System B, were to be compared for
accuracy. The amount of error between the miles the system reported and the miles that were
actually driven was found for each driver. 20 drivers are randomly assigned to use each of the
systems. Researchers will determine if there is a significant difference in the mean amount of
error between the two systems. Complete the design table below.
Research Design Table
Research Question:
Observational Study
Observational Experiment
Manipulative Experiment
Type of Research
What is the response variable?
What is the parameter that will be calculated?
Grouping/explanatory Variables 1 (if present)
Mean
Levels:
Proportion
Correlation
The hypotheses to be test are:
H0: μA = μB
H1: μA ≠ μB
α = 0.05
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Math& 146 Exam 3-4,
Closed notes, closed book, calculator ok
Page 3 of 4
1i. The data is the error for the system which is the difference in miles between what was driven
and what was reported by the electronic system. Is this data categorical or quantitative?
Circle 1: Categorical
Quantitative
The following errors were reported for cars using System A.
16
16
11
14
10
22
2
6
5
19
20
18
15
22
11
28
12
17
1j. Make a frequency distribution and a histogram of this data with a starting value of 0 and a
class width of 5. Use interval notation [ ) for your frequency distribution.
1k. What is the sample mean?
1k__________________
1l. What is the sample standard deviation?
1l__________________
1m. List the 5-number summary for the errors for cars using System A. Do NOT round any
numbers. Label the box plot completely. Include correct 5 number summaries, titles and axis
scales, correct graph.
Error for System A
Min
Q1
Median
Q3
Max
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Math& 146 Exam 3-4,
Closed notes, closed book, calculator ok
Page 4 of 4
1n. When system A was compared to system B, the p-value for this data is 0.038. Fill in the
blank for the concluding sentence. For n, use the total of those on system A and B.
At the 5% level of significance, there _______________a significant difference between System
A and System B (p = _______, n = ________).
2. Is there a correlation between the unemployment rate and the number of clients who use a
food bank?
Unemployment Rate
5.3
6.4
8.8
10.1
Clients
613
1357
982
1393
Make a complete scatter plot
2b. Find the correlation (using your calculator).
2b. Correlation_______________
3. Identify each of the following as a parameter or a statistic
3a.
µ
Parameter
Statistic
3b.
p̂
Parameter
Statistic
3c.
r
Parameter
Statistic
Parameter
Statistic
Parameter
Statistic
3c.
3c.
p
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