A group students collected data on the speed of vehicles traveling through a con
ID: 3064080 • Letter: A
Question
A group students collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed was 35 mph. The recorded speed (in mph) of 15 randomly selected vehicles is given below. You should be able to copy and paste them into Excel.
35
36
38
38
38
39
40
42
43
44
46
48
49
50
50
Use Excel Data Analysis to find the mean, median, and mode of the data set.
Assuming speeds are approximately normally distributed, use Data Analysis or StatPlus to construct a 95% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.
Construct a 99% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.
Compare the widths of the 95% and 99% confidence intervals.
What conclusions do you draw about the speeds people drive in this construction zone?
35
36
38
38
38
39
40
42
43
44
46
48
49
50
50
Explanation / Answer
Ans:
From above data:
mean=42.4
mode=38
median=42
sample standard deviation=5.193
n=15
df=15-1=14
1)critical t value for 95% CI=tinv(0.05,14)=2.145
95% confidence interval for mean
=42.4+/-2.145*5.193/sqrt(15)
=42.4+/-2.88
=(39.52, 45.28)
critical t value for 99% CI=tinv(0.01,14)=2.977
99% confidence interval for mean
=42.4+/-2.977*5.193/sqrt(15)
=42.4+/-3.99
=(38.41, 46.39)
99% confidence interval is wider as compared to 95% confidence interval.
As,lower limit of both intervals are higher than 35,so we can conclude that people drive at higer speed than the posted speed limit of 35.
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