p Values and 95% Confidence Interval

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Question: What's the difference between p value and 95% Confidence Interval (CI)?

Answer: They contain the same kernel of information, but the 95% CI contains more information.

Example:

The Odds Ratio (OR) for an infant dying because of Sudden Infant Death Syndrome was found to be 2.5 for households where the mother smoked cigarettes. The p value was < .05.
Three different studies showed the same Odds Ratio. They showed different CIs, however.

Study #1 showed an OR of 2.5 with a 95% CI from 2.4-2.6
Study #2 showed an OR of 2.5 with a 95% CI from 1.4-3.6
Study #3 showed an OR of 2.5 with a 95% CI from 0.4-5.6

What can you say from these results?

Studies 1 and 2 were "statistically significant," with a p value < .05. We know that because the CI does not include 1.
Study 3 included an OR of 1 in the 95% CI, and therefore the p value was not < .05.
Study 1 had a more precise estimate of the true OR, with a very small 95% CI.