1. A pharmaceutical company has specified that the variation in the quantity of active ingredient in its leading prescription medication must be such that the population standard deviation must be no more than 1.20 micrograms. The ingredient content of the pills is normally distributed. In a random sample of 20 pills, the standard deviation is found to be s 5 1.32 micrograms. Based on the sample data, use the a 5 0.05 level in testing H0: u # 1.20 micrograms versus H1: u . 1.20 micrograms.
2. During the early stages of production for a single-cylinder engine designed for use in portable gen- erators, the manufacturer randomly selects 12 engines from the end of the assembly line and subjects them to a battery of tests. In the horsepower tests, the engines are found to have an output standard deviation of s 5 0.18 horsepower. Assuming a normal distribution of horsepower outputs, determine the 90% confidence interval for u.