A group of Brigham Young University—Idaho students (Matthew Herring, Nathan Spen
ID: 3178151 • Letter: A
Question
A group of Brigham Young University—Idaho students (Matthew Herring, Nathan Spencer, Mark Walker and Mark Steiner) collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed was 25 mph. The recorded speed (in mph) of 14 randomly selected vehicles is: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40
a) Assuming speeds are approximately normally distributed, construct a 95% confidence Interval for the true mean speed of drivers in this construction zone. Interpret the Interval.
b) Construct a 99% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.
c) Compare the widths of the 95% and 99% confidence Intervals.
d) What conclusions do you draw about the speeds people drive in this construction zone?
Explanation / Answer
X
20
24
27
28
29
30
32
33
34
36
38
39
40
40
Mean =
32.1429
SD =
6.17510
Part A:
Confidence Interval:
X bar (-/+) E
X bar = 32.1429
E = Margin of Error
E = tc * ( s / sqrt (n)) = tc * ( 6.17510/sqrt(14))
tc is the critical value for 13 degrees of freedom at 5% level of significance is given by 2.160,
E = 2.160 *( 6.17510/sqrt(14)) = 3.5648
X bar (-/+) E
32.1429 (-/+)3.5648
28.58 and 35.71
The 95% confidence interval is (28.58 and 35.71)
Part B:
Confidence Interval:
X bar (-/+) E
X bar = 32.1429
E = Margin of Error
E = tc * ( s / sqrt (n)) = tc * ( 6.17510/sqrt(14))
tc is the critical value for 13 degrees of freedom at 1% level of significance is given by 3.012,
E = 3.012 *( 6.17510/sqrt(14)) = 4.9709
X bar (-/+) E
32.1429 (-/+)4.9709
27.17 and 37.11
The 99% confidence interval is (27.17 and 37.11)
Part C:
The width (95%) = 35.71 – 28.58 = 7.13
The width (99%) = 37.11 – 27.17 = 9.94
Part D:
The speed of 25 mph does not fall in between any of the above obtained confidence interval. We can conclude that almost all the vehicle’s driver in this construction zone crossing the standard speed level of 25 mph.
X
20
24
27
28
29
30
32
33
34
36
38
39
40
40
Mean =
32.1429
SD =
6.17510
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