Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of ancient Indian ruins in the southwestern United States. It is thought that Burnt Mesa Pueblo was occupied around ad 1300 (based on evidence from potsherds and stone tools). The following data give tree-ring dates (AD) from adjacent archaeological sites (Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by T. Kohler, Washington State University Department of Anthropology, 1992):

i. Use a calculator with mean and standard deviation keys to verify that = 1268 and s ‰ˆ 37.29 years.
ii. Assuming the tree-ring dates in this excavation area follow a distribution that is approximately normal, does this information indicate that the population mean of tree-ring dates in the area is different from (either higher or lower than) AD 1300? Use a 1% level of significance.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.
For degrees of freedom d.f. not given in the Student€™s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more €œconservative€ answer.

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