Problem 1. A mining company needs to estimate the average amount of copper ore per tonmined. A random sample of 50 tons give a sample means of 146.75 pounds. The populationstandard deviation is assumed to be 35.2 pounds. Give a 95% confidence interval for the average amount of copper in the population of tons mined. Also give a 90% confidence interval and a 99% confidence interval for the average amount of copper per ton. Problem 2. The manufacturer of batteries used in small electric appliances wants to estimate theaverage life of a battery. A random sample of 12 batteries yieldsx= 34.2 and s = 5.9 hours. Givea 95% confidence interval for the average life of a battery. Problem 3.A machine produces safety devices for use in helicopters. A qualitycontrolengineer regularly checks samples of the devices produced by the machine, and if too many ofthe devices are defective, the production process is stopped and the machine is readjusted. If arandom sample of 52 devices yields15defectives, give a 98% confidence interval for theproportion of defective devices made by this machine. Problem 4.An automobile manufacturer substitutes a different engine in cars that were knownto have an average miles-per-gallon rating of 31.5 on the highway. The manufacturer wants totest whether the new engine changes the miles-per-gallon rating of the automobile model. Arandom sample of 100 trial runs givesx= 29.8 miles per gallon and s = 6.6 miles per gallon.Using the 0.05 level of significance, is the average miles-per-gallon rating on the high way forcars using the new engine different from the rating for cars using the old engine? . Problem 5.S. Zesiger, in an article entitled Vetting the American Dream, claims that 85% of Corvette buyers are men. A study aimed at proving that p<0.85 looks at a random sample of 300Corvette owners and finds that 238 are men. Conduct the appropriate test, using= 0.05.

Problem 6.In a monthly briefing to the corporate office, the manager for the Embassy Suiteshotel in Atlanta report that the mean number of rooms rented out per night isat least212. Oneof the corporate officials fells that this number might be somewhat overstated. A sample of 150nights produces a mean of 201.3 rooms and a standard deviation of 45.5 rooms. If these results suggest the manager has padded his report, he will be severely admonished. At the 1 percent level, what is the managers fate?