A certain species of tree has an average life span of 130 years. A researcher has noticed that a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the width of the rings. Counting the rings allows the researcher to determine the age of each tree. 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 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.

a. Define the appropriate parameters and state the hypotheses for testing if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years.

b.

Describe how you would generate a single randomization sample in this situation and identify the statistic you would calculate for each sample.