Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 21

Provide the following information
(a) What is the level of significance State the null and alternate hypotheses.
(b) Check Requirements 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 you answers in part (a) to (c), will you reject or fail to reject the null hypothesis Are the data statistically significant at level
(e) Interpret your conclusion in the context of the application.
Note: For degree 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 "conservative" answer.
Archaeology: Tree Rings Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of prehistoric Indian ruins in the southwestern united State. It is thought that Burnt Mesa Pueblo was occupied around 1300 A.D. (based on evidence from potsherds and stone tools). The following data give tree-ring dates ( A.D. ) 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 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) that in 1300 A.D. Use a 1% level of significance.