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In: Statistics and Probability

Three engineers are independently estimating the spring constant of a spring, using the linear model specified...

Three engineers are independently estimating the spring constant of a spring, using the linear model specified by Hooke’s law. Engineer A measures the length of the spring under loads of 0, 1, 2, 4, and 6 lb, for a total of five measurements. Engineer B uses the same loads, but repeats the experiment twice, for a total of 10 independent measurements. Engineer C uses loads of 0, 2, 4, 8, and 12 lb, measuring once for each load. The engineers all use the same measurement apparatus and procedure. Each engineer computes a 95% confidence interval for the spring constant.

If the width of the interval of engineer A is divided by the width of the interval of engineer B, the quotient will be approximately

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