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Question
The quality control technician grew weary of measuring pistons that came off the line, so he decided to make a fixture that would tell him whether the piston fell within product specifications. The fixture had two holes, one the exact width of the upper specification (24 cm) and one slightly smaller than the lower specification (21 cm). If the piston fit through the smaller hole, it would be too small and therefore rejected. If the piston didn't fit through the larger hole, it was too large and would be rejected. Just to test his idea, he used the traditional measurement system and his new system on the next eight samples. The data and the two charts he constructed are shown below. Why aren't the plotted points forming similar shapes between the two graphs? Evaluate the advantages and disadvantages of his proposed system.
| Sample 1 | 29.5 | 23 | 20.9 | 24.9 |
| Sample 2 | 22.9 | 20.1 | 23.7 | 26.9 |
| Sample 3 | 25.9 | 23.6 | 23 | 24.3 |
| Sample 4 | 25.3 | 23.2 | 29.8 | 22.3 |
| Sample 5 | 24.7 | 25.1 | 20.6 | 23 |
| Sample 6 | 28.4 | 29.7 | 27.1 | 23.7 |
| Sample 7 | 21.9 | 23.5 | 24.9 | 24.2 |
| Sample 8 | 26.9 | 21.1 | 28.1 | 20.2 |
| Sample 9 | 25.5 | 27.6 | 26.3 | 27.2 |
| Sample 10 | 23.9 | 28.6 | 21.7 | 20.6 |
Answer
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