Ouch. I’ve made this mistake myself—confusing the CI of the mean with the CI of the predictive interval. It’s an easy mistake to make when you have very small data, because then both the predictive interval and the mean’s confidence interval will be wide. Much harder to misinterpret when you have decent amounts of data because the predictive interval typically won’t shrink much while the mean’s CI will become so narrow you can’t misinterpret it as being about the population.
Ouch. I’ve made this mistake myself—confusing the CI of the mean with the CI of the predictive interval. It’s an easy mistake to make when you have very small data, because then both the predictive interval and the mean’s confidence interval will be wide. Much harder to misinterpret when you have decent amounts of data because the predictive interval typically won’t shrink much while the mean’s CI will become so narrow you can’t misinterpret it as being about the population.