2. A group of Brigham Young University-Idaho students (Matthew Herring, Nathan S
ID: 3059726 • Letter: 2
Question
2. 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 given below 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40 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. a. 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
data is
20,24,27,28,29,30,32,33,34,36,38,39,40,40
Using technology,we get
x=32.143
=6.175
a)
CI = x ± Z/2 × (/n)
=32.143 ± 1.96 x (6.175/14)
=32.143 ± 3.23466
=32.143-3.23466 to 32.143+3.23466
=28.908 to 35.378
b)
CI = x ± Z/2 × (/n)
=32.143 ± 2.576 x (6.175/14)
=32.143 ± 4.25127
=32.143 - 4.25127 to 32.143 + 4.25127
=27.892 to 36.394
c)
Clearly,we see that 99% confidence interval is wider than 95% confidence interval
d)
Since posted speed limit is 25 and it doesnt lie in the confidence intervals
Hence people are jumping the speed limit
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