To increase the probability of detecting a significant change to 90%, which statement is correct?

• A. A smaller z-statistic decreases Type I error but reduces detection
• B. A larger z-statistic (like 3.34) can be used, but this increases the probability of a Type II error
• C. Z-statistic does not affect error rates
• D. A larger z-statistic reduces both Type I and Type II errors

Answer: (B)

The key idea is that the z-statistic threshold for declaring significance sets a balance between false positives and false negatives. Making the threshold larger (more extreme) makes the test more stringent. That reduces the chance of claiming significance when there isn’t a real change (lower Type I error), but it also makes it harder to detect a true change when one exists, increasing the chance of missing it (higher Type II error). Using a larger z-statistic, such as 3.34, exemplifies this trade-off: you’ll have fewer false alarms, but more real changes will fail to cross the threshold. The other statements misstate how the threshold affects error rates: a smaller threshold would raise Type I error, the z-statistic does influence error rates, and a larger threshold lowers Type I error but raises Type II error, not the opposite.