Dear Evans Ehourman,

The Fisher's Exact test tests whether the dimensions of your contingency table are independent - whether there is a relationship between sex and illness status.

In your case, the p-value from the Fisher's Exact Test is 0.06013, this value is more than 0.05 and therefore you should accept the null hypothesis which states that there is no relationship between sex and illness status.

If your p-value were < 0.05 (or you increased your alpha threshold) you would interpret the odds ratio as meaning women are 2.4311 times more likely to be ill than men.

Here are a couple of sites I tutorials I found describing the Fisher's Exact Test in R:

https://www.r-bloggers.com/contingency-tables-%E2%80%93-fisher%E2%80%99s-exact-test/

http://www.math.wustl.edu/~victor/classes/ma322/r-eg-21.txt

I hope this is useful.

Yours Faithfully,

Joseph Crispell