Based on anecdotal evidence, it was suspected that artificial hips made from ceramic had a mean time to failure that was 12 years. In order to investigate this suspicion, researchers followed a group of subjects of size n = 35 until their artificial hips failed. The group with ceramic hips had a sample mean lifetime of x = 12.4 years with a sample variance of s 2 = 2.9 squared years. (a) Conduct a statistical hypothesis test of H0 : = 12 versus Ha : 6= 12 using significance level = 0.05. (Clearly state all assumptions/theorems and show all your work) (b) Calculate a 95% two-sided confidence interval for the mean failure time for ceramic hips. (c) Explain how the computed confidence interval in part (b) can be utilized to make a statement regarding H0 : = 12.