A psychologist is studying the difference in average reaction times (in milliseconds) between two age groups. The data collected are: Group $1$ (Young Adults): ${\bar{x}}_1=245$, $s_1=15$, $n_1=6$; Group $2$ (Older Adults): ${\bar{x}}_2=278$, $s_2=22$, $n_2=8$. Construct an $80\%$ confidence interval for the difference in mean reaction times (Young Adults $-$ Older Adults). Assume unequal variances and approximately normal populations.