申論題

5. (20%) Company A and Company B are steel manufacturers. 25 steel specimens are obtained from each company to determine the yield strength. The result shows that the sample mean strength and sample standard deviation for Company A are 30.2 ksi and 4.0 ksi respectively. For Company B, the sample mean strength and sample standard deviation are 35.3 ksi and 5.0 ksi respectively.

(i) Construct a 95% confidence interval for the difference in the mean yield strength for the 2 companies. Assume normality for the distribution of yield strength. (10%)