A packing plant wants to see if their new packing machine works faster than the current machine. To test this hypothesis, they record the packing time for the next 10 packages for each machine. The results are shown in the table below: Old Machine 31.4 29.1 30.4 29.5 28.5 29.9 31.4 31.5 30.2 29.3 New Machine 33.8 33.0 35.7 34.1 32.9 33.2 31.9 34.1 34.0 30.2 a. Carry out a significance test to determine whether the new machine is faster at packing. [10 marks] b. Find a 95% confidence interval for the difference in mean packing time. What can you conclude? [5 marks]