Question

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 of those trees to count the number of rings and measure the widths 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 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.    

a. Define the appropriate parameter(s) 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.

c. Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.

d. Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.

e. What conclusion would you make at the 10% significance level?

Answer 1

assuming sd = 46.92

It is reasonable to use the t-distribution to perform a test about the average age of driftwood along this beach because we do not know the population variance.

If we know the population variance, we use normal distriubiton to perform a test.

Ho: mu=130

Ha: mu<130

The test statistic is

t=(xbar-mu)/(s/vn)

=(120-130)/(46.92/sqrt(27))

=-1.1074

p-value = P(t < TS)

= 0.139

since p-value > alpha (0.10)

we fail to reject the null hypothesis