A certain species of tree has an average life span of 130 ears. A researcher has notice a large number of trees of this species washing up along a beach as driftwood. She take core samples from 27 of those trees, seclected at random, to count the number of rins and measure the widths of the rings. condting the rings allows the researcher to determine the age of each tree. The mean age of the sampled driftwood is 119 years old, with standard deviation 46.92 years. She wants to determine if the sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree.
a) Verify that it is reasonable to use the t-distribution to perform a test about the average age of driftwood along this beach.
b) Test, at the 5% level, if thers is evidence that the average age of driftwood along this beach is significantly below 130 years. Include all of the details of the test.