Business Context
VoltEdge manufactures printed circuit boards and uses automated circuit analysis to detect electrical faults before shipment. A process engineer claims a new inspection setting reduces the defect rate versus the current setting.
Problem Statement
Use the inspection results below to determine whether the new circuit-analysis setting produces a statistically significant reduction in the proportion of defective boards.
Given Data
| Group | Boards Inspected | Defective Boards | Observed Defect Rate |
|---|
| Current setting (control) | 2,400 | 168 | 7.0% |
| New setting (treatment) | 2,100 | 105 | 5.0% |
Assume the engineer wants to test for a reduction in defect rate at a significance level of 5%.
Requirements
- State the null and alternative hypotheses.
- Compute the sample defect rates for both groups.
- Calculate the pooled defect rate under the null hypothesis.
- Compute the standard error for a two-proportion z-test.
- Calculate the z-statistic and the one-tailed p-value.
- Decide whether the new setting significantly reduces defects at α=0.05.
- Briefly explain what circuit analysis means in this manufacturing context and interpret the result for the business.
Assumptions
- Boards were independently sampled from comparable production runs.
- The only material process change was the circuit-analysis inspection setting.
- Sample sizes are large enough for the normal approximation to apply: both defect and non-defect counts exceed 10 in each group.
- This is a one-sided test because the business question is specifically whether the new setting lowers the defect rate.
