The article “Modeling of Urban Area Stop-andGo Traffic Noise” presents measurements of traffic noise, in

nicekikah 2021-01-22 Answered

The article “Modeling of Urban Area Stop-andGo Traffic Noise” presents measurements of traffic noise, in dBA, from 10 locations in Bangkok, Thailand. Measurements, presented in the following table, were made at each location, in both the acceleration and deceleration lanes.
\(\begin{array}{|c|c|}\hline \text{Location} & \text{Acceleration} & \text{Decelaration} \\ \hline 1 & 78.1 & 78.6 \\ \hline 2 & 78.1 & 80.0 \\ \hline 3 & 79.6 & 79.3 \\ \hline 4 & 81.0 & 79.1 \\ \hline 5 & 78.7 & 78.2 \\ \hline 6 & 78.1 & 78.0 \\ \hline 7 & 78.6 & 78.6 \\ \hline 8 & 78.5 & 78.8 \\ \hline 9 & 78.4 & 78.0 \\ \hline 10 & 79.6 & 78.4 \\ \hline \end{array}\)
Can you conclude that there is a difference in the mean noise levels between acceleration and deceleration lanes?

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jlo2niT
Answered 2021-01-23 Author has 96 answers

Step 1
Given: n=10
Let us assume: α=5%=0.05
Given claim: Difference μd q 0
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesisi and the alternative hypothesis state the opposite of each other.
H0 : μd=0
Hα : μd q 0
Determine the difference in value of each pair.
Sample 1Sample 2Difference D78.178.60.578.1801.979.679.30.38179.11.978.778.20.578.1780.178.678.6078.578.80.378.4780.479.678.41.2Mean0.17sd1.0122
Step 2
Determine the sample mean of the differences. The mean is sum of all values divided by number of values.
d=0.5  1.9 + 0.3 +  0.3 + 0.4 + 1.210  0.17
Determine the sample standard deviation of the differences:
sd=(0.5  0.17)2 +  + (1.2  0.17)210  1  1.0122
Determine the value of the test statistic:
t=dsdn=0.171.012210  0.531
The P-value is the probability of obtaining the value of the test statistic, or a value more extreme, assuming that the null hypothesis is true. The P-value is the number (or interval) in the column title of the Students T distribution in the appendix containing the t-value in the row df=n  1=10  1=9 (Note: We double the boundaries, because the test is two-tailed).
0.50=2 × 0.25 < P < 2 × 0.40=0.80
If the P-value is less than the significance level, reject the null hypothesis.
P > 0.10=10%  Fail  reject H0
There is sufficient evidence to support the claim that is a difference in the mean noise levels between accelaration and decelaration lanes.

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