Braking Distance Exploration Lab 2023
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Portland Community College *
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Date
Feb 20, 2024
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Math 243 Braking Distance Lab
Automobile Braking
Continental Tire Company is considering a newly designed tread pattern for its all-weather tires.
Tests have indicated that these tires will provide better gas mileage and longer tread life. The last remaining test is for braking effectiveness. The company hopes the tire will allow a car travelling at 60 mph to come to a complete stop within an average of 125 feet after the brakes are applied. They will adopt the new tread pattern unless there is evidence that the tires do not
meet this objective. The distances (in feet) are in the file “BrakingDistance.xlsx” in the D2L.
1.
What is the research question
in this situation? (What would you or the researchers be interested in here?)
2.
What are the observational units
in this scenario? 3.
What is the Response Variable (the variable of interest)? 4.
Is the Response Variable type Categorical
or Numerical
?
5.
What is the sample mean
of the braking distance – using correct unit of measure - for this new tire tread design at 60 mph? x̅
= _____ ___
6.
Include a screenshot documenting your work below:
*** First Classroom Checkpoint
– Go to our D2L Navbar and select “Surveys”. Start the “Braking Distance” Survey and answer question #1 to check that you have the correct sample mean. You may just leave the Survey open for use throughout this Lab Activity***
7.
Describe (in words) what the symbol µ
represents with this scenario. Page 1
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Math 243 Braking Distance Lab
8.
Assuming this is a two-sided
hypothesis test
; State (
formally
) the Null and Alternative hypotheses.
9.
Use the R/C Theory-Based Inference One Mean applet
to determine the (approximate) two-sided
p-value. p-value
= ______________
*** Second Classroom Checkpoint – Go to the survey and answer question #2. You may just leave the survey open for use throughout this Lab Activity***
10.
Take a screenshot
of your Theory-Based Inference applet and paste it (neatly) below. Be sure to include the p-value in your screenshot
:
11.
Based on the two-sided p-value you reported above, does 125 ft appear to be a plausible value
for µ (the long-run Mean of braking distances)
? Explain your reasoning
.
12.
How would this two-sided p-value compare to a one-sided p-value: larger
, smaller
, or the same
? Explain why you chose this answer.
Using the Plausible Values Method
to determine the 95% Confidence Interval
Page 2
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Math 243 Braking Distance Lab
13.
Use the R/C Theory-Based Inference applet for One Mean
, repeatedly testing other possible values for µ, to determine plausible values and construct a 95% confidence interval
for µ
(in a similar fashion, using the table to record your data as demonstrated in class). Mean (µ) under H
0
125.1 ft
125.2 ft
125.3 ft
125.4 ft
125.5 ft
125.6 ft
125.7 ft
(Two-sided) p-value
Reject or plausible?
Mean (µ) under H
0
128.2 ft
128.3 ft
128.4 ft
128.5 ft
128.6 ft
128.7 ft
128.8 ft
(Two-sided) p-value
Reject or plausible?
14.
State AND Interpret
the 95% confidence interval for this situation.
a.
( _____ , _____ )
b.
Interpret the 95% confidence: “I am 95% confident that _____________(
context of scenario here – briefly
) is between _____ (
lower endpoint with correct unit of measure
) and _____ (
upper endpoint with correct unit of measure
)
15.
*** Third Classroom Checkpoint – Go to the survey and answer question #3. You may just leave the survey open for use throughout this Lab Activity***
16.
Should Continental Tire adopt the new tread pattern? What does your confidence interval suggest?
Be sure to fully explain your conclusion
.
Let’s say the Continental Tire Company agreed to a 99% confidence interval, and that you’re the head of the customer safety department. First, what is the new confidence interval? Page 3
of 5
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Math 243 Braking Distance Lab
Let’s use the Plausible Values Method.
Using the Plausible Values Method
to determine the 99
% Confidence Interval
17.
Now, using the R/C Theory-Based Inference applet for One Mean
, repeatedly test possible values for µ to determine plausible values and construct a 99% confidence interval for µ
.
18.
What alpha (significance level) will you be using for this new confidence interval? _______ (hint: remember this, we’re using 99% confidence level).
Create your table below similar (but not the same as!) to the table above – and be sure to construct a NEW 99%
confidence interval
! Mean (µ) under H
0
(Two-sided) p-value
Reject or plausible?
Mean (µ) under H
0
(Two-sided) p-value
Reject or plausible?
19.
Then state AND interpret
the 99%
confidence interval for this situation.
c.
( _____ , _____ )
d.
Interpret the 99% confidence: “I am 99% confident that _____________(
context of scenario here – briefly
) is between _____ ___ (
lower endpoint with correct unit of measure
) and _____ ___ (
upper endpoint with correct unit of measure
)
Using the Threoretical Method
to determine the 99%
Confidence Interval
Page 4
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Math 243 Braking Distance Lab
Because we have a large enough sample size here, the Plausible Values Method
should produce very similar results to the Theoretical approach
. In such a case, the theory-based approach is often the most convenient, especially if our confidence level is not 95%.
Go to the same Theory-Based Inference applet
and use the same sample data we’ve been using. Then select the “
Confidence interval
” button on the lower right side of the applet and change the confidence level
in the applet from 95% to 99%
and press the Calculate CI
button. 20.
Report the 99%
confidence interval given by the “Confidence interval” section of the applet.
( _____ , _____ )
21.
Paste a screenshot of the applet below (be sure to include the Confidence Interval):
*** Fourth Classroom Checkpoint – Go to the survey and answer question #4. You may just leave the survey open for use throughout this Lab Activity***
22.
How close are the endpoints from the 99% Plausible Values Method
Interval to the 99% Theoretical
Interval endpoints? 23.
Based on this new interval, what would be your decision (remember, you’re responsible for consumer safety
)? Fully explain your decision based on the evidence.
*** Please be sure to answer the last 2 Survey questions since these questions will help me get a better understanding of how I can better help you.
Page 5
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