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, 3, 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, 6, 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.
a. 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
b. If the width of the interval of engineer A is divided by the width of the interval of engineer C, the quotient will be approximately
c. Each engineer computes a 95% confidence interval for the length of the spring under a load of 2.5 lb. Which interval is most likely to be the shortest? Which interval is most likely to be the longest?