To find the critical value \( t_{\alpha/2} \) that corresponds to a confidence level of 82.6%, we first need to calculate \( \alpha \):
\[ \alpha = 1 - 0.826 = 0.174 \]
Since we are looking for the value \( t_{\alpha/2} \), we need to divide \( \alpha \) by 2:
\[ \alpha/2 = 0.174 / 2 = 0.087 \]
Next, we need to find the degrees of freedom, which is computed as:
\[ df = n - 1 = 79 - 1 = 78 \]
Now, we look up the critical value \( t_{\alpha/2} \) for \( \alpha/2 = 0.087 \) with 78 degrees of freedom using a t-table or a calculator.
Using a t-table or calculator, we find the critical value corresponding to \( t_{0.087} \) and \( df = 78 \).
Using statistical software or tables, we find:
\[ t_{0.087} \approx 1.375 \]
Thus, rounding to three decimal places, the value is:
\[ t_{\alpha/2} \approx 1.375 \]
So, the final answer is:
\[ \boxed{1.375} \]