A tech‐industry poll surveys $500$ software developers and finds $380$ of them prefer to write unit tests before coding new features. The team uses $300$ bootstrap replicates to estimate a $99\%$ confidence interval for the true proportion of all developers who follow this practice. From the bootstrap distribution, the $2.5$^th percentile is $0.730$ and the $97.5$^th percentile is $0.795$. Compute the normal‐approximation $99\%$ interval and compare it to the bootstrap result. 

$99\%$ CI:

The bootstrap CI () is entirely contained within the normal approximation CI, indicating the normal method is slightly more conservative

$99\%$ CI:

The bootstrap CI’s lower bound ($0.730$) exceeds the normal CI’s lower bound ($0.701$), but its upper bound ($0.795$) is above the normal CI’s upper bound ($0.763$), suggesting the bootstrap is both shifted upward and narrower

$99\%$ CI:

The bootstrap CI () is wider than the normal CI on both ends, implying that the normal approximation underestimates uncertainty

$99\%$ CI:

The bootstrap CI’s upper bound ($0.795$) exceeds the normal CI’s upper bound ($0.699$), indicating the bootstrap captures heavier tails than the normal method