If data collection for a defect rate is extended to two months, what is the expected effect on the power of the test?

Extending the data collection period for a defect rate generally leads to an increase in the sample size, as more data points are gathered over the two months. A larger sample size enhances the reliability of the test results and reduces the standard error of the mean, which contributes to greater statistical power.

In hypothesis testing, power is the probability that the test will correctly reject a false null hypothesis. With increased sample size due to extended data collection, the test becomes more capable of detecting a true effect when it exists, thus improving the likelihood of identifying significant differences or defects in the data. This enhancement of the test’s ability to detect real differences signifies an increase in power.

While there could be circumstances where no effect or other outcomes might seem plausible, typically, extending the duration of data collection directly correlates with an increase in sample size which in turn increases the test's power.