A fish-processing company is concerned about the shelf life of its new cat food. A quality manager claims that the mean product shelf life of cans from the Dartmouth facility is less than the advertised mean (of 12 months) for its product's shelf life. Test that claim using the 0.005 level of significance. A sample of 40 items produced in Dartmouth had a mean shelf life of 11 months, and a standard deviation of 1.52 months.