The life in hours of a heating element used in a furnace is known to be approximately

normally distributed with N01, 0'2). A random sample of 35 heating elements is selected and found to have a sample average life E = 561.14 hours. The standard deviation is known and equal to a = 16.23 hours. At the level of a = 0.05, test the hypotheses H0 : ,u = 550 versus H1 : p > 550. What is your conclusion? (Justify your answer mathematically.)