Consider again Problem 10.1.18 where 62 insulators of a certain type were tested at 180 C. and it was found that 13 had a dielectric breakdown strength below a specified threshold level. In addition. 70 insulators of the same type were tested at 250 C, and it was found that 20 had a dielectric breakdown strength below the specified threshold level.
(a) Conduct a one-sided hypothesis test to investigate whether this experiment provides sufficient evidence to conclude that the probability of an insulator of this type having a dielectric breakdown strength below the specified threshold level is larger at 250 C than it is at 180 C.
(b) Construct a two-sided 99% confidence interval for the difference between the probabilities of an insulator of this type having a dielectric breakdown strength below the specified threshold level at 180oC and at 250oC