9.54 An electric circuit contains three resistors, each of a different type. Tests on 10 type I resistors showed a sample mean resistance of 9.1 ohms with a sample standard deviation of 0.2 ohm;

tests on 8 type II resistors yielded a sample mean of 14.3 ohms and a sample standard deviation of 0.4 ohm; whereas tests on 12 type III resistors yielded a sample mean of 5.6 ohms and a sample standard deviation of 0.1 ohm. Find a 95% confidence interval for , the expected resistance for the circuit. What assumptions are necessary for your answer to be valid?