Chapter 10.3, Problem 20P

Archaeology: Cultural Affiliation "Unknown cultural affiliations and loss of identity at high elevations ” These are words used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric people tended not to take trade wares to temporary settings and/or isolated areas (Source: Prehistoric Ne w Mexico: Background for Surrey, by D. E. Stuart andR. P Gauthier. University of New Mexico Press). As elevation zones of prehistoric people (in what is now the state of New Mexico) increased, there seemed to be a loss of artifact identification. Consider the following information:

Elevation Zone	Number of Artifacts	Number Unidentified
7000-7500 ft	112	69
5000-5500 ft	140	26

Let $p_1$ be the population proportion of unidentified archaeological artifacts at the elevation zone 7000-7500 ft in the given archaeological area. Let p. be the population proportion of unidentified archaeological artifacts at the elevation zone 3000-5500 ft in the given archaeological area.

(a) Find a 99% confidence interval for $p_1-p_2.$

(b) Interpretation Explain the meaning of the confidence interval in part (at in the context of this problem Does the confidence interval contain all positive numbers? all negative numbers? both positive and negative numbers? What does this tell you (at the 99% confidence level) about the population proportion of unidentified artifacts at high elevations (7000- 7500 ft) compared with the population proportion of unidentified artifacts at lower elevations (5000-5500 ft) ? How does this relate to the stated hypothesis?