Problem

Machine A has mean production time \(12.1~s\) and range \(1.0~s\); machine B has mean \(12.0~s\) and range \(4.5~s\). Treat mean differences at most \(0.2~s\) as operationally similar. Compare the centers and spreads and state the operational conclusion.

Source statistical display: Production times: machine A mean12.1s,range1.0s; B mean12.0s,range4.5s. Treat mean differences ≤0.2s as operationally similar. No requested comparison or classification is annotated.

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mean difference=|12.1−12.0|=0.1≤0.2s, so A clearly slower; range difference=4.5−1.0=3.5s, so B less consistent; conclusion=A is slower despite the tolerance

mean difference=|12.1−12.0|=0.1≤0.2s, so typical times are similar; range difference=4.5−1.0=3.5s, so A less consistent because its mean is larger; conclusion=similar times with A more variable

mean difference=|12.1−12.0|=0.1≤0.2s, so B faster; range difference=4.5−1.0=3.5s, so B more consistent because range is larger; conclusion=B faster and more consistent

mean difference=|12.1-12.0|=0.1≤0.2s, so typical times are operationally similar; range difference=4.5-1.0=3.5s, so B is less consistent; conclusion=similar typical time, much greater variation for B

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Machine A has mean production time \(12.1~s\) and range \(1.0~s\); machine B has mean \(12.0~s\) and range \(4.5~s\). Treat mean differences at most \(0.2~s\) as operationally similar. Compare the centers and spreads and state the operational conclusion.

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