Nurse workshop .08 (95%CI .032 to .188)

Standard care .16 (95%CI .083 to .285)

Was the rate of ED visits for hypoglycemic events statistically significantly different at .05 level between the two groups? YES or NO

How do you know?

My thought answer is "NO" because: The way to determine if things are statistically significant is by calculating a p-value. The confidence interval is an identified range of possible values “p” might take. Because the point estimate falls within the confidence interval, it is an automatic accepted (not rejected) p-value. Since both of the point estimates fall within their CI, the two groups are not significantly different.

Is this correct? Am I thinking about this all wrong?