The following output (from MINITAB) describes the fit of a linear model y = β0 +β1x +ε that expresses the length of a spring in cm (y) in terms of the load upon it in kg (x). There are n = 15...

The following output (from MINITAB) describes the fit of a linear model y = β0 +β1x +ε that expresses the length of a spring in cm (y) in terms of the load upon it in kg (x). There are n = 15 observations.

a. How many degrees of freedom are there for the Student’s t statistics?

b. Find a 98% confidence interval for β1.

c. Find a 98% confidence interval for β0.

d. Someone claims that if the load is increased by 1 kg, that the length will increase by exactly 0.35 cm. Use the given output to perform a hypothesis test to determine whether this claim is plausible.

e. Someone claims that the unloaded (load = 0) length of the spring is more than 1.5 cm. Use the given output to perform a hypothesis test to determine whether this claim is plausible.