I would start by stating things more formally, e.g. (with no prior information):
The null hypothesis is that these two samples come from the same population. The alternative is that they come from different populations where one really has more "hits".
A simple and traditional approach would be Fisher's exact test.
Wiki should allow you to calculate it manually for your data.
R you could do something like this:
> cm1 <- matrix(c(53, 67, 29, 38),
nrow = 2,
dimnames = list(c("first", "control"), c("hits", "misses")))
> addmargins(as.matrix(cm1), c(1,2))
hits misses Sum
first 53 29 82
control 67 38 105
Sum 120 67 187
p=1 meaning probability of your data given the null is very high (suggests that first group v. unlikely to be different from control).
You can also do
The null hypothesis is that these two samples come from the same
population. The alternative is that the first comes from a different
population which has more "hits" than the second.
... but it's still
Now there are other methods but most will accept that it's unlikely that there's any great difference between
53/82 = 65% and
67/105 = 64%