Answered: Steel Carbon Commutes 30 26 Mean (min)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Bicycle frames can be made from carbon, steel, or other
materials. Carbon frames are much more expensive than
steel, but they are also much lighter. Could this lighter

frame have a significant impact on speed? In 2010 a doc-
tor in England, who commutes daily to work 27 miles

roundtrip on a bicycle, ran his own randomized experi-
ment to investigate.

Each day for several months Dr. Groves flipped a coin to
determine whether he would ride his steel frame bicycle or
his carbon frame bicycle to work and back. He rode a total
of 30 journeys on the steel frame bike and 26 journeys on
his carbon frame bicycle, recording his total commuting
time for each day. The summary statistics are shown below:a) Why would you prefer to see the actual data before
proceeding with inference?
b) Construct and interpret a 95% confidence interval for
the difference in average commuting times.
c) Explain in this context what “95% confidence”
means.
d) Based on your confidence interval, do the doctor’s
data provide evidence that there’s a difference in
average commuting time for the two bikes? Explain.

Steel
Carbon
Commutes
30
26
Mean (min) 107.80
109.35
SD (min)
4.90
6.25
Source: Groves, Jeremy. “Bicycle Weight and Commuting
Time: A randomized Trial," Significance: Statistics
Making Sense, June 2011, Volume 8 Issue 2: 95-97.

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