To find the degrees of freedom ([tex]\(df\)[/tex]) where [tex]\(df\)[/tex] is defined as the smaller of [tex]\(n_1 - 1\)[/tex] and [tex]\(n_2 - 1\)[/tex], and we have [tex]\(n_1 = 122\)[/tex] and [tex]\(n_2 = 119\)[/tex], we can follow these steps:
1. Calculate [tex]\(n_1 - 1\)[/tex]:
[tex]\[
n_1 - 1 = 122 - 1 = 121
\][/tex]
2. Calculate [tex]\(n_2 - 1\)[/tex]:
[tex]\[
n_2 - 1 = 119 - 1 = 118
\][/tex]
3. Determine the smaller value between [tex]\(121\)[/tex] and [tex]\(118\)[/tex]:
[tex]\[
\min(121, 118) = 118
\][/tex]
Therefore, the degrees of freedom ([tex]\(df\)[/tex]) is:
[tex]\[
df = 118
\][/tex]
