We are 95% confident that the true population mean is between 0.4758903, 0.6735586.

That is, if we were to take 100 random samples, we would expect at least 95% of those samples to have a mean within 0.4758903, 0.6735586.

ci <- data.frame(mean=numeric(), min=numeric(), max=numeric())
for(i in seq_len(100)) {
samp <- sample(pop, size=30)
se <- sd(samp) / sqrt(length(samp))
ci[i,] <- c(mean(samp),
mean(samp) - 2 * se,
mean(samp) + 2 * se)
}
ci$sample <- 1:nrow(ci)
ci$sig <- ci$min < 0.5 & ci$max > 0.5