In an inertia welding experiment, a sample of 50 welds made with a standard welding method were tested. The sample mean and sample standard deviation of the breaking strengths of these welds were found to be 94 ksi and 3 ksi, respectively. Another sample of 60 welds using an alternative welding method were also tested and the resulting sample mean and sample standard deviation were 96 ksi and 3.5 ksi, respectively.

(a) Construct a 95% confidence interval for the difference in true mean breaking strengths for the two types of welds.
(b) Is there evidence that there exists a difference in the true mean breaking strengths for the two types of welds? Use the five-step hypothesis testing procedure in answering this question. The confidence level is 95%. (Optional)