A factory producing light bulbs has made a recent change in the production process that will be less costly. The fear is that the mean life of the bulbs produced under the new process may be lower than it was before the change. Based upon historical records, it is known that the average lifetime of the bulbs produced before the change was 400 hours. The engineers in the plant are confident that only the mean might be affected by the change. A random sample of 55 light bulbs from the new process are selected and used until they burn out. The mean life of this sample was 350 hours and the standard deviation was 45. Using this sample do the following.

Find a 95% confidence interval for the mean life of the bulbs produced from the new process.