If you're not satisfied by the "inter ocular trauma test" (a difference that hits you between the eyes) and you really, really want a null hypothesis significance test then you'll have to handle the fact that, although the data isn't very far from Normal (within groups), the variance is far from homogenous.
The missing value for Outside (NaN) suggests that the data is paired, else you wouldn't have included it. We could look at 'Inside - Outside' but the missing value reduces us to 7 cases. The difference isn't very far from Normal
so I'd be reasonably happy with a one-sample T-test of the null hypothesis that the difference is zero (this is identical to a paired T-test).
If you want to use all the data you'll have to ignore any pairing. To overcome the non-homogenous variance I'd use a non-parametric test, e.g.
Edited to add:
@Bernhard correctly commented that Wilcoxon's signed rank test is the common non-parametric alternative to the paired T-test. For completeness, here is that test with confidence interval. Because it's paired it only uses 7 pairs.
Edited to add:
@KieranCraddock commented "There are 8 points in each group, each corresponding to 8 compass point directions. Does this mean paired t test is most appropriate?"
On consideration, OH DEAR!!! This may invalidate any statistical significance test. Such tests assume that the observations are random, independent, samples from a population. If that were the case a single observation would consist of two values, one inside one outside. We have 8 observations (one has a missing value) and we might chart the data like this.
But you say the pairs aren't random, they correspond to compass point directions. Arbitrarily assigning compass points we might then chart the data like this.
A single observation now consists of 16 values, 8 inside and 8 outside, We only have one observation. We have no way of estimating the variation between repeated observations. We cannot apply any statistical significance test or calculate any confidence intervals.