Three types of a metal alloy were investigated to see how much damage they suffered when subjected to a high temperature. A total of 220 samples were obtained for each alloy, and after being subjected to the high temperature, the damage was classisfied as "none."' "slight," "medium," or "severe." Out of the 220 samples of type 1, 98 had no damage, 32 had slight damage, 48 had medium damage, and 42 had severe damage. Out of the 220 samples of type II. 52 had no damage, 27 had slight damage, 67 had medium damage, and 74 had severe damage. Out of the 220 samples of type III. 112 had no damage, 35 had slight damage, 41 had medium damage, and 32 had severe damage.
(a) Perform a hypothesis test to assess whether there is sufficient evidence to conclude that the three alloys are not all equivalent in terms of the damage that they suffer.
(b) Perform a hypothesis test to assess whether there is sufficient evidence to conclude that the probability of suffering severe damage is different for alloy type I and alloy type III.
(c) Construct a 99% confidence level two-sided confidence interval for the probability that a sample of alloy type II will not suffer any damage.