## 4 Results  
By conducting paired hypothesis tests to compare the performance of the vital sign metrics for older adults with the implementation of the sensor network, it was found that, as in previous studies [4], all nine metrics (breathing frequency (BF), deep sleep (DS), snoring (S), heart rate (HR), heart rate variability (HRV), oxygen saturation (OS), REM sleep (REMS), temperature (T), total sleep time (TST)) generally improved significantly. Table 4 shows the p-value results of the paired hypothesis tests conducted. The frequencies of improvements in the experiment participants are analyzed in Table 5, which shows the observed counts of older adults who improved in each performance metric with the use of the sensor network. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & \(\mathbf{p}\)**-Value** & **Test** \\ \hline Deep sleep & 0.000 & [PERSON] \\ \hline Heart rate & 0.006 & \(t\)-test \\ \hline Breathing frequency & 0.000 & \(t\)-test \\ \hline Temperature & 0.000 & [PERSON] \\ \hline REM sleep & 0.000 & [PERSON] \\ \hline Oxygen saturation & 0.004 & [PERSON] \\ \hline Heart rate variability & 0.000 & \(t\)-test \\ \hline Snoring & 0.000 & [PERSON] \\ \hline Total sleep time & 0.000 & [PERSON] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of the paired hypothesis tests [4]. Considering that, for all variables, 50% of the people would randomly improve and 50% would not, the chi-square was calculated (see Equation (1)) for each metric and for the entire table overall. Table 6 shows the chi-square calculation for each metric. \[\chi^{2}=\sum_{i=1}^{n}\frac{(O_{i}-E_{i})^{2}}{E_{i}} \tag{1}\]  
where  
\(\chi^{2}\) is the chi-square value. \(O_{i}\) is the observed frequency of metric \(i\). \(E_{i}\) is the expected frequency of metric \(i\). The critical chi-square value for the table of variables with a significance level of 0.05% and 8 degrees of freedom is 15.50731306, which is exceeded by the sum of the chi-square values for each variable, which is 262.24. The null hypothesis of independence is rejected, indicating that there are associations between the variables. The critical chi-square value with a significance level of 0.05% for each of the variables is 3.841458821, indicating that all variables except oxygen saturation had significant differences between the expected and observed values. With these chi-square test results, it is confirmed that by following the advice of the sensor network, the adult participants in the experiment improved in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & \(\chi^{2}\)**Improved** & \(\chi^{2}\)**Not Improved** & **Total \(\chi^{2}\)** \\ \hline Breathing frequency (BF) & 6.48 & 6.48 & 12.96 \\ \hline Deep sleep (DS) & 6.48 & 6.48 & 12.96 \\ \hline Snoring (S) & 8 & 8 & 16 \\ \hline Heart rate (HR) & 2 & 2 & 4 \\ \hline Heart rate variability (HRV) & 33.62 & 33.62 & 67.24 \\ \hline Oxygen saturation (OS) & 1.62 & 1.62 & 3.24 \\ \hline REM sleep (REMS) & 24.5 & 24.5 & 49 \\ \hline Temperature (T) & 30.42 & 30.42 & 60.84 \\ \hline Total sleep time (TST) & 18 & 18 & 36 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Chi-square calculations for each metric. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **Improved** & **Not Improved** & **TOTAL** \\ \hline Breathing frequency (BF) & 68 & 32 & 100 \\ \hline Deep sleep (DS) & 68 & 32 & 100 \\ \hline Snoring (S) & 70 & 30 & 100 \\ \hline Heart rate (HR) & 60 & 40 & 100 \\ \hline Heart rate variability (HRV) & 91 & 9 & 100 \\ \hline Oxygen saturation (OS) & 59 & 41 & 100 \\ \hline REM sleep (REMS) & 85 & 15 & 100 \\ \hline Temperature (T) & 89 & 11 & 100 \\ \hline Total sleep time (TST) & 80 & 20 & 100 \\ \hline TOTAL & **670** & **230** & **900** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Observed improvement data by metric with the use of the sensor network. breathing frequency, deep sleep, snoring, heart rate, heart rate variability, REM sleep, temperature, and total sleep time.