A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 trees to determine their ages. The average age of the trees in the sample is approximately 120 years. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging. Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. Required:
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.