The following contingency table shows inspection records for 650 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).
Decision Experience
Low Medium High
Pass 164 286 99
Fail 18 59 24
a-1. How many of the units passed inspection?
a-2. How many of the units failed inspection?
b. How many of the units were inspected by inspectors with high experience?
c. What proportion of the units were inspected by inspectors with low experience? (Round your answer to 2 decimal places.)
d. What proportion of the units were inspected by inspectors with medium experience and failed inspection? (Round your answer to 2 decimal places.)
a-1. The number of units that passed inspection is 164 + 286 + 99 = 549.
a-2. The number of units that failed inspection is 18 + 59 + 24 = 101.
b. The number of units inspected by inspectors with high experience is 99 + 24 = 123.
c. The proportion of units inspected by inspectors with low experience is (164 + 18)/650 = 0.2769 or 27.69%.
d. The proportion of units inspected by inspectors with medium experience and failed inspection is 59/650 = 0.0908 or 9.08%.
a-1. To find how many units passed inspection, we need to look at the "Pass" category in the contingency table. According to the table, 164 units passed inspection.
a-2. To find how many units failed inspection, we need to look at the "Fail" category in the contingency table. According to the table, 18 units failed inspection.
b. To find how many units were inspected by inspectors with high experience, we need to look at the "High" row in the contingency table. According to the table, 99 units were inspected by inspectors with high experience.
c. To find the proportion of the units inspected by inspectors with low experience, we divide the total number of units inspected by inspectors with low experience by the total number of units inspected.
The total number of units inspected by inspectors with low experience is 164 (from the "Pass" category) + 18 (from the "Fail" category) = 182.
The total number of units inspected is 164 (from the "Pass" category) + 18 (from the "Fail" category) + 286 (from the "Medium" row) + 59 (from the "Medium" row) + 99 (from the "High" row) + 24 (from the "High" row) = 650.
The proportion of units inspected by inspectors with low experience is 182/650 = 0.28 (rounded to 2 decimal places).
d. To find the proportion of the units inspected by inspectors with medium experience and failed inspection, we divide the number of units in the "Fail" category and the "Medium" row by the total number of units inspected.
According to the table, 59 units were inspected by inspectors with medium experience and failed inspection.
The proportion of units inspected by inspectors with medium experience and failed inspection is 59/650 = 0.07 (rounded to 2 decimal places).