Let's say we do a poll/survey for $n=250$ people, and we study a variable in a Likert scale with 7 possible values (-3 to +3):

Person    Subgroup     Question1
1         B            -3 (strongly disagree)
2         C            0 (neutral)
3         A            2 (agree)
4         A            1 (slightly agree)
5         E            -2 (disagree)
...       ...          ...
250       A            3 (strongly agree)

We want to evaluate/test the hypothesis:

"People from subgroup A tend to have a significantly higher agreement with Question1 (i.e. higher value for Question1 in Likert scale) than the general population."

This is an unprecise "handwaving" formulation. Question:

1. How should we reformulate this hypothesis more precisely to be able to use usual statistical hypothesis testing tools, and be able to reject or not reject the hypothesis with $p = 0.05$, $p=0.01$, etc.?

2. Which common statistical hypothesis testing tools can be used in such situation?

   I know the $\chi^2$ fit test to see if an observation matches a fixed distribution; or also the $\chi^2$ test for homogeneity or independance; but none of these seem to apply here

Let's say we do a poll/survey for $n=250$ people, and we study a variable in a Likert scale with 7 possible values (-3 to +3):

Person    Subgroup     Question1
1         B            -3 (strongly disagree)
2         C            0 (neutral)
3         A            2 (agree)
4         A            1 (slightly agree)
5         E            -2 (disagree)
...       ...          ...
250       A            3 (strongly agree)

We want to evaluate/test the hypothesis:

"People from subgroup A tend to have a significantly higher agreement with Question1 (i.e. higher value for Question1 in Likert scale) than the general population."

This is an unprecise "handwaving" formulation. Question:

1. How should we reformulate this hypothesis more precisely to be able to use usual statistical hypothesis testing tools, and be able to reject or not reject the hypothesis with $p = 0.05$, $p=0.01$, etc.?

2. Which common statistical hypothesis testing tools can be used in such situation?

   I know the $\chi^2$ fit test to see if an observation matches a fixed distribution (goodness of fit); or also the $\chi^2$ test for homogeneity or independance; but none of these seem to apply here.
   Or does it apply?
   Or should one use other tests? I often hear about t-test, Fisher, Kruskal-Wallis, ANOVA, Dunn, so I was curious which one to use here.