We would like to check the ink production for two different production processes, say process 1 and process 2 to see whether there is a difference in the mean density of ink produced between the two processes. A sample of size 10 from both processes is taken. Process 1 has sample mean of 14.8 and a sample standard deviation of 1.4. Process 2 has sample mean of 15.6 and a sample standard deviation of 1.7. Assuming normality for both processes with same population standard deviation:

(a) Perform a hypothesis test to check if both production processes produce ink with equal densities (Use the test statistic and assume = 0.05)

(b) Find the two-sided confidence interval for the difference in mean of ink densities. Can you draw the same conclusion as in part (a) from this confidence interval?

(c) How does the solution for part (a) change if the we assume that the two populations have different variances?