A data scientist at a high-volume semiconductor manufacturing plant is responsible for monitoring a critical etching process. They use hypothesis testing to decide if the process has deviated from its specifications. The null hypothesis (H0) is that the process is operating within specification, while the alternative hypothesis (H1) is that it has deviated. A deviation could result in producing millions of faulty microchips. To minimize production interruptions from false alarms, the team has chosen a very low significance level (alpha), such as 0.001, for their control tests.
Which of the following statements best describes the primary risk associated with this statistical strategy?
By lowering the significance level, the team decreases the probability of a Type I error (falsely concluding the process has deviated), but this simultaneously increases the probability of a Type II error, elevating the risk of not detecting a true deviation and consequently shipping defective products.
A low significance level increases the statistical power (1 - β) of the test, thereby reducing the probability of both Type I and Type II errors simultaneously.
The chosen alpha level directly minimizes the risk of shipping defective products by ensuring that the process is only stopped for statistically significant, genuine deviations.
This strategy correctly minimizes the most critical risk, which is the Type II error (failing to detect a deviation), by making the test more sensitive to any anomalies.
The correct answer explains the fundamental trade-off between Type I and Type II errors. A Type I error, or false positive, occurs when a true null hypothesis is rejected. In this scenario, it means stopping production when the process is actually fine (a false alarm). The probability of a Type I error is equal to the significance level, alpha (α). By setting a very low alpha, the team reduces the chance of this error.
A Type II error, or false negative, occurs when a false null hypothesis is not rejected. Here, it means failing to detect that the process has deviated when it actually has. For a fixed sample size, lowering the probability of a Type I error (alpha) inevitably increases the probability of a Type II error (beta, β). Given the high cost of a Type II error in this context-shipping millions of faulty microchips-the strategy of setting an extremely low alpha elevates the most significant business risk.
Incorrect options misunderstand these relationships. One distractor falsely claims this strategy minimizes the Type II error. Another incorrectly states that a low alpha increases statistical power; in reality, lowering alpha decreases power (Power = 1 - β). The final distractor is misleading because while it correctly states that a low alpha reduces false alarms, it incorrectly concludes this minimizes the risk of shipping defects, ignoring the increased risk of a Type II error.
Ask Bash
Bash is our AI bot, trained to help you pass your exam. AI Generated Content may display inaccurate information, always double-check anything important.
What is the trade-off between Type I and Type II errors in hypothesis testing?
Open an interactive chat with Bash
Why does lowering the significance level (alpha) decrease statistical power?
Open an interactive chat with Bash
How do Type I and Type II errors impact real-world decisions in manufacturing?