The dielectric breakdown strength of an electrical insulator is defined to be the voltage at which the insulator starts to leak detectable amounts of electrical current, and it is an important safety consideration. In an experiment. 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.
(a) Conduct a 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 than 5%.
(b) Construct a one-sided 95% confidence interval ihat provides a lower bound on the probability of an insulator of this type having a dielectric breakdown strength below the specified threshold level.