Explain Type I and Type II errors and the trade-offs between them.

A Type I error (false positive) occurs when the null hypothesis is rejected when it is actually true. A Type II error (false negative) occurs when we fail to reject the null hypothesis even though the alternative is true.

Reducing $α$ (Type I error rate) makes it harder to detect an effect, which increases $β$ (Type II error rate). Thus, there's a trade-off between minimizing false positives and false negatives.

Context determines which error to minimize. For example, airport security prioritizes avoiding false negatives (missing threats), while the justice system aims to avoid false positives (wrongly convicting the innocent). In tech: Meta may prioritize avoiding false negatives in harmful content detection, while false positives may be more critical in ad targeting.