An experiment was conducted to investigate how the corrosion properties of chilled cast iron depend upon the chromium content of the alloy. A collection of n = 12 samples of chilled cast iron with 0.1% chromium content provided corrosion rates with a sample mean of  = 2.462 and a sample standard deviation of sx = 0.315, while a collection of m = 13 samples of chilled cast iron with 0.2% chromium content provided corrosion rates with a sample mean of  = 2.296 and a sample standard deviation of sy = 0.297.
(a) Conduct a hypothesis test to investigate whether there is any evidence that the chromium content has an effect on the corrosion rate of chilled cast iron.
(b) Construct a 99% two-sided confidence interval for the difference between the average corrosion rates of chilled cast iron at the two chromium contents.