(15 points) On August 23, 2016, Nathan Eovaldi, a member of the New York Yankees at the time, had Tommy John Surgery to repair his Ulner Collateral Ligament in his elbow. Many baseball pitchers need this surgery because of the stress pitching puts on the elbow. It has been found that some pitchers, after receiving the surgery, come back to throw FASTER than they did before the surgery. According to a study performed on Eovaldi before the surgery, it was found that the Population Mean speed of Nathan Eovaldi fastballs was 96.4 mph. In 2018, as a member of the World Champion Red Sox, and after the Tommy John Surgery, a sample of 37 Nathan Eovaldi fastballs had a Sample Mean speed of 97.0 mph. For the problem, assume that the Population Standard Deviation is 1.6 mph. Let x = the continuous random variable for the possible speed of a Nathan Eovalid Fastball. Is there sufficient statistical evidence at a 1% level of significance to conclude that the Population Mean speed of a Nathan Eovaldi fastball has INCREASED ; that the surgery has indeed allowed Eovaldi to now THROW FASTER? Round decimals accordingly based on the variable and table you are using. Draw the Normal Curve and SHADE STEP 1 Statements STEP 1 Level of Significance a = the appropriate tail. Label the percentage in the tail. STEP 2 Calculate the Sample Test Statistic Use the appropriate Formula STEP 3 Calculate P - Value Write Proper Probability Notation Round to an appropriate number of decimal places Use the Proper Table Write your solution in the appropriate form STEP 4 State your Conclusion Use Graph or Algebra to help confirm STEP 5 Interpretation B.O.O.S. Level of Significance inclusion Make sure to write your conclusion based on the appropriate Hypothesis