## 3 Results
### Comparison of MT Vs. MNT Treatments  
In this study, a paired-sample \(t\)-test was used due to the characteristics of the experimental design where the capacitance measurements for the MT and MNT sensors were obtained using the same waste samples, which establishes a direct dependency relationship between the observations. This implies that the observations in both groups are not independent, but are directly related, since each pair of data corresponds to the same waste sample evaluated by both sensors. The paired-sample \(t\)-test is appropriate in this case because it evaluates whether the mean of the differences between the measurements of the MT and MNT sensors is significantly different from zero. This approach allows controlling the variability between the samples, focusing only on the differences attributable to the performance of the sensors. Additionally, although the \(t\)-test requires that the differences between pairs follow an approximately normal distribution, this criterion was met after verifying the normality of the data using graphical and statistical methods, ensuring that the results obtained are valid and reliable to establish significant differences between the sensors evaluated. Since the differences between measurements presented a verifiable normal distribution, the use of the paired \(t\)-test was the most appropriate choice, allowing reliable results to be obtained with greater sensitivity to detect significant differences between the sensors evaluated. Let \(X_{i}\) and \(Y_{i}\) represent the recorded capacitance values (the most relevant characteristic) for MT and MNT sensors, respectively, with \(d_{i}\)= \(X_{i}-Y_{i}\) denoting the difference between the samples. To assess whether the MNT sensor shows superior performance compared to the MT sensor, the following hypotheses are posed:  
\[H_{o}:\ \mu_{x}\leq\mu_{y}\]  
\[H_{a}:\ \mu_{x}>\mu_{y}\]  
where \(\mu_{x}\) and \(\mu_{y}\) are the means corresponding to the capacitance values obtained during the sampling campaigns for the two types of MT and MNT sensors, respectively. The \(H_{o}\) hypothesis states that MNT is better than the MT and the \(H_{a}\) establishes the opposite condition. To accept or reject the proposed hypotheses, it is necessary to perform a hypothesis contrast on the difference in means with paired sampling, using the so-called paired t-test. For this, the following steps are established [27]:  
Step 1: A new random variable \(Z=X-Y\) is defined and the mean value and standard deviation for the variable \(Z\) are calculated. The result of this process yielded the values of \(-111.28\) and \(217.816\) for \(\overline{Z}\) and \(S_{z}\), respectively. On the other hand, when defining a new variable Z, it is necessary to make an adjustment in the hypotheses as follows:  
\[H_{o}:\ \mu_{x}\leq\mu_{y}\rightarrow\mu_{x}-\mu_{y}\leq 0\rightarrow\mu_{z}\leq 0\]  
\[H_{a}:\ \mu_{x}>\mu_{y}\rightarrow\mu_{x}-\mu_{y}>0\rightarrow\mu_{z}>0\]  
Step 2: We proceed to calculate the value of the statistic established for the test by using the following expression:  
\[d=\frac{\overline{Z}}{S_{z}}\sqrt{n}=\frac{-111.28}{214.816}\sqrt{100}=-5.180\]  
where \(d\) is the value of the statistic and \(n\) obeys the number of samples for the two proposed scenarios. Step 3: Establish the acceptance range of the \(H_{o}\) for \(\left\{t:t<T_{(\alpha n-1)}\right\}\) at 5% significance (\(\alpha=0.05\)) and \(n-1\) degrees of freedom. For the particular case, the value of \(T(0.05;99)=1.6603\), defining the range of acceptance of the \(H_{o}\) between \((-\infty,1.6603)\). When evaluating the value of the \(d\) statistic, it is observed that it is within the acceptance interval, which is why \(H_{o}\) is not rejected. In view of the above, it is concluded that the sensor supported in the MNT is better than the MT sensor for the proposed scenario, with 95% confidence.