Dr. Razz, CEE Department, is conducting an experiment on a new nano graphite tub

Question

Dr. Razz, CEE Department, is conducting an experiment on a new nano graphite tube composite building material. Prototype design of the initial composite material was based on a thickness of 25 mm. After numerous optimizations, he concluded that the maximum tensile strength could be achieved by reducing the thickness precisely to 20 mm from the initial 25 mm specification. s) To verify his optimization results [of preferring 20 mm thickness], test specimens were fabricated, 18 samples each from 25 mm and 20 mm prototype designs, tested and tensile strengths (N/m2) were measured at the CEE Structural Lab as shown below. Preliminary statistical analysis indicated that the mean tensile strengths from both prototype designs distribute approximately normal at the 95% confidence level. 25 mm Prototype 20 mm Prototype 18 1.06 N/m2 0.09 N/ 1.12 N/m2 0.12 N/m2 Subsequently, Lab test result indicated that the 20 mm thickness prototype did increase the mean tensile strength of the composite material significantly compared to the 25 mm thickness prototype with a 95% level of confidence. Now, before finalizing his conclusion, Dr. Razzaq would like to be absolutely sure by checking the magnitude of variability/dispersion in the two prototypes' tensile strengths. Find a 95% CI for the magnitude of variability in these two prototype designs. Interpret your conclusion in form of a recommendation - should thickness prototype (over 25 mm) as his final design? Why and Why not? Dr. Razzaq choose the 20 mm

Explanation / Answer

Dr. Razz, CEE Department, is conducting an experiment on a new nano graphite tube composite building material. Prototype design of the initial composite material was based on a thickness of 25 mm. After numerous optimizations, he concluded that the maximum tensile strength could be achieved by reducing the thickness precisely to 20 mm from the initial 25 mm specification. s) To verify his optimization results [of preferring 20 mm thickness], test specimens were fabricated, 18 samples each from 25 mm and 20 mm prototype designs, tested and tensile strengths (N/m2) were measured at the CEE Structural Lab as shown below. Preliminary statistical analysis indicated that the mean tensile strengths from both prototype designs distribute approximately normal at the 95% confidence level. 25 mm Prototype 20 mm Prototype 18 1.06 N/m2 0.09 N/ 1.12 N/m2 0.12 N/m2 Subsequently, Lab test result indicated that the 20 mm thickness prototype did increase the mean tensile strength of the composite material significantly compared to the 25 mm thickness prototype with a 95% level of confidence. Now, before finalizing his conclusion, Dr. Razzaq would like to be absolutely sure by checking the magnitude of variability/dispersion in the two prototypes' tensile strengths. Find a 95% CI for the magnitude of variability in these two prototype designs. Interpret your conclusion in form of a recommendation - should thickness prototype (over 25 mm) as his final design? Why and Why not? Dr. Razzaq choose the 20 mm

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