3. A manufacturing company is considering changing to a new more economical steel supplier. The main requirement states that the yield stress at tension of steel must be at least 252 MPa with 95 % confidence. In order to determine whether the new supplier satisfies this requirement, a series for 12 tensile tests are performed and the following measurements are recorded; 252.575. 255.168. 246.982, 253.224, Yield Stress 252.138. 248.885. 250.633, 252.185, (MPa) 258.657. 257,039, 248.800. 257.570 The mean and standard deviation of the sample are 252.821 MPa and 3.712 MPa, respectively a) Would you recommend the change in steel suppliers? Start your solution by clearly stating the null and alternative hypotheses, show all your calculations and then clearly state the criterion used to arrive to the conclusion. Word your conclusion properly, do not just say reject or fail to reject. Answers without these elements will be graded as zero. ) Provide a 95 % confidence interval (20 pts.) Use a level of significance of a = 0.05