Appropriate Statistical Test? (Combining survey responses such as age groupings and Likert items) Is there a statistical test for the following sort of survey result?
A survey was sent out asking about levels of satisfaction (sadly, it lacked a neutral option). I combined the responses in a pivot-table with age-groups of the respondents (which sadly aren't evenly distributed).

+-------------+---------------------+-----------------------+--------------------+------------------+-------------+
|  Age Range  | Highly dissatisfied | Somewhat dissatisfied | Somewhat satisfied | Highly satisfied | Grand Total |
+-------------+---------------------+-----------------------+--------------------+------------------+-------------+
| 25-29       |                     |                       |                  3 |                  |           3 |
| 30-39       |                   4 |                    18 |                 27 |               10 |          59 |
| 40-49       |                   3 |                    25 |                 56 |               14 |          98 |
| 50-59       |                   8 |                    20 |                 66 |               12 |         106 |
| 60-65       |                   2 |                    10 |                 34 |               15 |          61 |
| 65+         |                   1 |                     8 |                 27 |                7 |          43 |
| under 25    |                   1 |                       |                  8 |                  |           9 |
| Grand Total |                  19 |                    81 |                221 |               58 |         379 |
+-------------+---------------------+-----------------------+--------------------+------------------+-------------+


Are there any statistical tests that may draw additional insights here? In particular, I'm trying to identify if age of the sample group may indicate any significant bearing on "dis-satisfaction".
Non-mathematician here, so many thanks in advance for any help.
 A: Chi-squared Test of Independence
A chi-squared test for independence of age group
and dissatisfaction vs. satisfaction would be
be appropriate, provided you are willing to ignore
the ordinal character of age groups. I will provide
an outline of the analysis.
Contingency table. There are so few subjects in age groups Under 25 and
25-29 that it seems prudent to combine them. Also,
according to the wording your question, I combined 'strongly' and 'somewhat' dissatisfied
categories (also the two satisfied categories).
Data can be entered into R as follows to make the
required matrix of counts:
d = c(1,22,28,28,9)
t = c(12,59,98,106,61)
s = t - d
MAT=rbind(d, s)
MAT
  [,1] [,2] [,3] [,4] [,5]
d    1   22   28   28    9
s   11   37   70   78   52

You should check my summarization and data entry.
The method will be sufficiently clear to repeat
if you should need to make changes.
Chi-squared test. Then the results of chisq.test in R are as shown
below. Other kinds of software will provide similar
results.
chisq.test(MAT, sim+T)

        Pearson's Chi-squared test

data:  MAT
X-squared = 10.156, df = 4, p-value = 0.03789

Warning message:
In chisq.test(MAT, sim + T) : 
Chi-squared approximation may be incorrect

Validity of test. The warning message results from an expected count
for 'dissatisfied' in the youngest age group.
The chi-squared statistic has approximately a chi-squared distribution with 4 degrees of freedom, provided that
all expected counts are at least 5.
The one cell mentioned
above has a count above 3, which some authors say is
OK, if the vast majority of cells have counts above 5.
According to this, the P-value < 0.05 can be taken
as evidence of association (lack of independence) between
age and dissatisfaction.
Looking at expected counts: You can find the formula for computing the ten expected counts $E_{ij}$ in your textbook to verify the claims above.
Simulation in R: When some expected counts may be too small, the implementation of chisq.test in R permits simulation
of the true P-value (without reference to the chi-squared
distribution). Results from simulation are as follows,
showing that the P-value above is approximately correct.
chisq.test(MAT, sim=T)

        Pearson's Chi-squared test 
        with simulated p-value 
        (based on 2000 replicates)

data:  MAT
X-squared = 10.156, df = NA, p-value = 0.03848

Ad hoc comparisons. Because there is evidence in MAT of association
between age groups and dissatisfaction, you may want
to look at cells where agreement of expected counts
$E_{ij}$ and observed counts $X_{ij}$ is especially poor.
Then perhaps do ad hoc tests using two-by-two tables
to see if you can say which age groups (or combinations
thereof) are mainly responsible for rejection of
the null hypothesis of independence. (the second youngest 30-39 and oldest age groups of MAT seem worthy of particular attention.)
Perhaps see this related Q&A.
