Is the difference in the outcome for black and white women statistically significant?

No. The proper way of testing this is by using Fisher's exact test. Quite simple in one line of R:

fisher.test(matrix(c(36, 11, 38, 16), nrow=2))

Running this shows we obtain such a difference (77% vs. 70%) with about 50% probability just due to chance, given the sample size. The output of the R command above is:

data: matrix(c(36, 11, 38, 16), nrow = 2)

p-value = 0.5081

alternative hypothesis: true odds ratio is not equal to 1

95 percent confidence interval:

0.5175229 3.7540626

sample estimates:

odds ratio

1.373629