The CDC also published something recently on our infant mortality:
http://www.medscape.com/viewarticle/551734
The infant mortality rate among non-Hispanic black Americans is 13.60 per 1,000 -- twice the death rate within 1 year of birth than for white and Hispanic babies.
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This is an interesting example of a statistic out of context, since it doesn't include the relative living conditions, diet, and access to health care of the various populations, nor the patterns of drug use. Without that information, the statistic is meaningless. Also, did it include illegal immigrant Hispanic populations, or just US citizens?
Just to illustrate, Hispanic populations, if Illegals are factored in, have a similar standard of living and access to health care when compared to Black Americans. So what causes the dramatic discrepancy? Drug use? Black Americans have higher rates of certain types of drug use than Hispanics (and non-Hispanic caucasians). Diet? I believe (though I can't find numbers to back this up) that Black Americans tend to have worse dietary habits in general.
There is also the issue of teen pregnancies, which have higher rates of low birth weights and related health problems. Black Americans have a teen pregnancy rate that is over twice that of non-Hispanic caucasians, and 30-50% higher than that of Hispanics.
Not to mention STD rates, which are, depending on the STD, between a few times and a few dozen times higher among Black Americans than among caucasians, Hispanic and non-. Rates of gonorrhea are astronomical among Black Americans in general by comparison to any other population. Syphilis rates are up to 5 times higher. Rates of genital herpes are considerably higher among Black Americans, with black females double the infection rate of caucasian females. Rates of congenital STDs (babies born with STDs), another major factor for infant death, are similarly high. 69% of all HIV positive females in the US are black.
(Sources: NIH, CDC)
Context changes the meaning of a statistic dramatically. That is why I tend to dislike Moore's work. His statistics are generally accurate; but he manipulates the context to encourage false conclusions. As for the the infant mortality statistic, it's clearly not closely correlated with access to healthcare, but rather a problem of much greater complexity, involving diet, age, STDs, and drug use.