Answer
$lower~critical~value\lt r\lt upper~critical~value$: null hypothesis is not rejected.
There is not enough evidence to conclude that the residuals are not random.
Work Step by Step
$H_0:~The~sequence~is~random$ versus $H_1:~The~sequence~is~not~random$
$n=12$, $n_A=7$, $n_B=5$ and $r=5$
Small sample case:
$lower~critical~value=3$
$upper~critical~value=11$
(According to table X, for $n_1=7$, $n_2=5$)
Test statistic: $r=5$
Since $lower~critical~value\lt r\lt upper~critical~value$, we do not reject the null hypothesis.
