NZ Scholarship Statistics Practice Questions - New Zealand Scholarship Statistics Assessment Exam

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When constructing a 95% bootstrap confidence interval for a highly skewed population using the percentile method, why is the percentile method preferred over a symmetric formula (Sample Mean ± 1.96 × SE)?

The bootstrap percentile method naturally reflects skewness by allowing asymmetric distance from the point estimate to the lower and upper bounds The symmetric formula is mathematically invalid for sample sizes under 10,000 regardless of skewness The percentile method forces the bootstrap distribution to transform into a standard normal curve Symmetric intervals always overestimate the population median by exactly two standard errors

Correct Answer:

The bootstrap percentile method naturally reflects skewness by allowing asymmetric distance from the point estimate to the lower and upper bounds

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