1 (30 points): An article in Quality Engineering described an experiment on a grinding wheel. The following table shows grinding force data (N) at two different vibration levels (low and high): Helpful numbers: t0.10,11=1.363 t0.05,11=1.796 t0.025,11=2.201 t0.01,11=2.718 t0.005,11=3.106IE 4362 Problem 1 2IE 4362 Problem 1 3IE 4362 Problem 1 4IE 4362 Problem 1 5 1. (16 points) Does mean grinding force increase with vibration level? Use formal hypothesis testing to determine your answer.IE 4362 Problem 1 6 2. (5 points) If you were to model grinding force distribution for the high level of vibration, could you say grinding force is normally distributed? Provide an explanation, including numbers, from the JMP output. 3. (9 points) Find the 90% confidence interval for grinding force at the high vibration level. Explain how you could use this information for production planning (e.g., what could you tell upper management about the performance of the grinding wheel?)