A manufacturer claims that the mean lifetime, μ, of its light bulbs is 49 months. The standard deviation of these lifetimes is 6 months. Ninety bulbs are selected at random, and their mean lifetime is found to be 47 months. Can we conclude, at the 0.01 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 49 months? Perform a two-tailed test.