An electrical firm manufactures light bulbs that have a mean length of life that is approximately normally distributed. The mean life of the bulb is stated as 800 hours. A random sample of sixteen bulbs had a mean life of 775.8 hours with a variance of 1600. Use the appropriate test with alpha = 0.01 to determine if we can conclude that the mean life of the bulbs is smaller than 800 hours? Write the conclusion in the context of the problem including the test statistic and observed significance level.