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

Step 1
Given: ${\displaystyle n=10}$
Let us assume: ${\displaystyle \alpha =5\mathrm{\%}=0.05}$
Given claim: Difference ${\displaystyle {\mu }_d\ne q0}$
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesisi and the alternative hypothesis state the opposite of each other.
${\displaystyle H_0:{\mu }_d=0}$
${\displaystyle H_{\alpha }:{\mu }_d\ne q0}$
Determine the difference in value of each pair.
$\begin{array}{|ccc|}\hline \text{Sample 1}& \text{Sample 2}& \text{Difference D}\\ 78.1& 78.6& -0.5\\ 78.1& 80& -1.9\\ 79.6& 79.3& 0.3\\ 81& 79.1& 1.9\\ 78.7& 78.2& 0.5\\ 78.1& 78& 0.1\\ 78.6& 78.6& 0\\ 78.5& 78.8& -0.3\\ 78.4& 78& 0.4\\ 79.6& 78.4& 1.2\\ \text{Mean}& & 0.17\\ \text{sd}& & 1.0122\\ \hline\end{array}$
Step 2
Determine the sample mean of the differences. The mean is sum of all values divided by number of values.
${\displaystyle \bar{d}=\frac{-0.5-1.9+0.3+\cdots -0.3+0.4+1.2}{10}\approx 0.17}$
Determine the sample standard deviation of the differences:
${\displaystyle s_d=\sqrt{\frac{{(-0.5-0.17)}^2+\cdots +{(1.2-0.17)}^2}{10-1}}\approx 1.0122}$
Determine the value of the test statistic:
${\displaystyle t=\frac{\bar{d}}{\frac{s_d}{\sqrt{n}}}=\frac{0.17}{\frac{1.0122}{\sqrt{10}}}\approx 0.531}$
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 ${\displaystyle df=n-1=10-1=9}$ (Note: We double the boundaries, because the test is two-tailed).
${\displaystyle 0.50=2\times 0.25<P<2\times 0.40=0.80}$
If the P-value is less than the significance level, reject the null hypothesis.
${\displaystyle P>0.10=10\mathrm{\%}\Rightarrow Fail\to reject{H}_0}$
There is sufficient evidence to support the claim that is a difference in the mean noise levels between accelaration and decelaration lanes.