Thermal endurance tests were performed to study the relationship between temperature and lifetime of polyester enameled wire (“Thermal Endurance of Polyester Enameled Wires Using Twisted Wire Specimens,” IEEE Trans. Insulation, 1965: 38–44), resulting in the following data.

Temp. | 200 200 200 200 200 200 Lifetime | 5933 5404 4947 4963 3358 3878 Temp. | 220 220 220 220 220 220 Lifetime | 1561 1494 747 768 609 777 Temp. | 240 240 240 240 240 240 Lifetime | 258 299 209 144 180 184

a. Does a scatter plot of the data suggest a linear probabilistic relationship between lifetime and temperature?

b. What model is implied by a linear relationship between expected ln(lifetime) and 1/temperature? Does a scatter plot of the transformed data appear consistent with this relationship?

c. Estimate the parameters of the model suggested in part

(b). What lifetime would you predict for a temperature of 220?

d. Because there are multiple observations at each x value, the method in Exercise 14 can be used to test the null hypothesis that states the model suggested in part

(b) is correct. Carry out the test at level .01.