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2. The ultimate tensile strength of steel is being tested by a mechanical engineer. He testes 42 specimens and obtains sample mean and variance are 420 MPa and 100 MPa, respectively. (a) What is the 16: = 90% two-side condence interval of the mean ultimate tensile strength? ( 10 points) (b) How many additional tests are needed to cut the condence interval width in part (a) by half? (10 points)