Use the given sample data and confidence level to produce and interpret an appropriate confidence interval. In your narrative, include the Central Limit Theorem (CLT) Check, the margin of error calculation, and a correct interpretation of the confidence interval in the given context.

The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a male. As of this writing, 291 babies were born to parents using the XSORT method, and 239 of them were boys. Use an 98% confidence level.