STAT 230 KPU Flexure of Concrete Beams Reinforced with Advanced Composite Orthogrids Worksheet

I’m working on a statistics question and need an explanation to help me learn.

3. In a batch chemical process, two catalysts are compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1 and a sample of 10 batches was obtained using catalyst 2. The 12 batches for which catalyst 1 was used gave a sample mean yield of 85 with a sample standard deviation of 4, while the 10 batches for which catalyst 2 was used gave a sample mean yield of 81 with a sample standard deviation of 5. Let µ₁ and µ₂ denote the true mean yields using catalysts 1 and 2, respectively. Compute the 99 % confidence interval for µ₁ − µ₂, assuming that the data are normally distributed.

4. The article ”Flexure of Concrete Beams Reinforced with Advanced Composite Orthogrids” (J.

of Aerospace Engr., 1997) gave the accompanying data on ultimate load (kN) for two different types of beams.

Assuming that the underlying distributions are normally distributed. Using the Welch procedure method to calculate and interpret a 90 % confidence interval for the difference between true average load for the carbon beams and that for the fiberglass beams (µ₂ − µ₁).