The following contingency table shows inspection records for 630 units of a particular product. The records have been cross-classified by the inspector’s decision (Pass and Fail) and the inspector’s experience (Low, Medium, and High).
Experience
Decision Low Medium High
Pass 152 287 103
Fail 16 46 26
a.) How many of the units passed inspection? How many of the units failed inspection?
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b.) How many of the units were inspected by inspectors with high experience?
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c.) What proportion of the units were inspected by inspectors with low experience?
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d.) What proportion of the units were inspected by inspectors with medium experience and failed inspection?
Sample Answer
Sample Answer
a.) To determine how many units passed inspection, we add up the values in the “Pass” row: 152 + 287 + 103 = 542. Therefore, 542 units passed inspection.
To determine how many units failed inspection, we add up the values in the “Fail” row: 16 + 46 + 26 = 88. Therefore, 88 units failed inspection.
b.) To determine how many units were inspected by inspectors with high experience, we add up the values in the “High” column: 103 + 26 = 129. Therefore, 129 units were inspected by inspectors with high experience.
c.) To determine the proportion of units inspected by inspectors with low experience, we divide the total number of units inspected by inspectors with low experience (152) by the total number of units (630): 152 / 630 ≈ 0.2413. Therefore, approximately 0.2413 (or 24.13%) of the units were inspected by inspectors with low experience.
d.) To determine the proportion of units inspected by inspectors with medium experience and failed inspection, we divide the number of units inspected by inspectors with medium experience and failed inspection (46) by the total number of units (630): 46 / 630 ≈ 0.0730. Therefore, approximately 0.0730 (or 7.30%) of the units were inspected by inspectors with medium experience and failed inspection.
