QUESTION 4 

(a) A random sample of 6 steel beams has a mean compressive strength of 58392 psi (pound per square inch) with its population standard deviation is 648 psi. Use this information and the level of significance α = 0.05 to test whether the true average compressive strength of steel from which this sample came is 58000 psi.

b) Past data indicate that the variance of measurements made on sheet metal stampings by experienced quality control inspectors is 0.18 (inch)2 . Such measurements made by an inexperienced inspector could have too large a variance (perhaps because of inability to read instruments properly) or too small a variance (perhaps because unusually high or low measurements are discarded). If a new inspector measures 101 stampings with variance of 0.13 (inch)2 , test at the 0.05 level of significance whether the inspector is making satisfactory measurements. Assume data is normally distributed.