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?
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?
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 5 images
