The authors have developed a numerical-based engineering ethics case study for use in engineering courses. It has been shown that ethics case studies that involve technical calculations and real-world situations appeal more to engineering students than do purely qualitative cases. The case is a fictionalized account of several incidents that the second author witnessed while employed at a steel manufacturing company. In this study, students are asked to evaluate several coils of steel and determine which ones meet certain minimum standards for yield strength. Statistical analysis is necessary to evaluate the strength of the steel. Test data is given for each of the steel coils, from one to five test samples per coil. After analysis, the students are presented with several scenarios and asked to decide which coils meet the minimum standards. In making the decision to approve coils for shipment, students must decide on the appropriate statistical measures to use and in particular how much of the confidence interval needs to be above the minimum standard. The students are then asked several questions concerning how their knowledge, or lack of knowledge, of the ultimate use of the steel affects their decision-making process. Should the engineer have different standards for different applications? Even though the calculations involved in this problem are relatively simple, the problem the students are presented with does not have an easy answer. This case study is appropriate for a sophomore-level materials or mechanics of materials course, however, with a short introduction to material properties, it could also be used in an introductory statistics course.