Enrichment of mutations in particular region of the gene I have a gene say "X" of 3000 base pairs. 300 of those 3000 bp belong to ring domain. Rest 2700 do not belong to ring domain. In a particular tumor, the ring region has 4 alterations and the rest of the region has 4 alterations too. Clearly the frequency in ring region is higher, but is there a statistical test that will give me a p value that tells the probability of having a mutation in ring region is higher or not?
 A: As I wrote in comments, I don't know how complicated your question is. Maybe I'm exaggerating a bit with those models or you don't know anything else about the situation.
If that is question should be very simple (homework or something like that) you could have a look on simplest Welch's T test.
With this test you could check wheter two non-overlapping populations have the same means.
Let's say, you have two populations $\mathfrak{F}$ (RING - foreground) and $\mathfrak{B}$ (the rest - background) represented by two arrays of lengths $L_F = 300$ and $L_B = 2700$, respectively. In the picture below, with blue balls are marked positions of bases which were altered.

For array $\mathfrak{F}$ we have independent binary random variables $F_1, \dots, F_{L_F}$, where $F_i = 1$ denotes at this position $i$ an alternation took place. I assume that any position in $\mathfrak{F}$ the probablity of alternation is the same(, but unknown) $p_f$ and each variable $F_i$ denotes single Bernoulli trial, so $F_i \sim Bernoulli(p_f)$.
For array $\mathfrak{B}$ we have the same situation, but corresponding variables $B_1, \dots, B_{L_B}$ are distributed with maybe different probablity $p_b$, so $B_i \sim Bernoulli(p_b)$.
According to the Central Limit Theorem (we have more than 30 random variables with each array, so CLT may be used) the mean of $F_i$s and mean of $B_i$s have Normal distribution:
$$\text{(mean of $F_{i}$)} ~~~~~~ \mu_F =\frac{\sum\limits_{i} F_i}{L_F} \sim Normal(p_f, \frac{p_f \cdot (1 - p_f)}{L_F} )$$
$$\text{(mean of $B_{i}$)} ~~~~~~ \mu_B = \frac{\sum\limits_{i} B_i}{L_B} \sim
Normal(p_b, \frac{p_b \cdot (1 - p_b)}{L_B})$$
Because you don't know anything about variations, thus use Welch's T test https://en.wikipedia.org/wiki/Welch's_t_test (rather than Student's T test).
In this test you may compare the corresponding means with hypotheses:
$$H_0 : \mu_F = \mu_B ~~ \text{against} ~~ H_A: \mu_F > \mu_B$$
In R you use method t.test{stats}:
t.test(arr_f, arr_b, alternative = "greater", paired = FALSE, var.equal = FALSE)
arr_f and arr_b are simply an 0-1 arrays where 1 points to alternated bases and 0 elsewhere.
The two trailing parameters are by default false, but I put them to make you aware of them. The last var.equal = FALSE indicates the Welch's T test instead of Student's T test with TRUE.
