“Unknown cultural affi­liations and loss of identity at high elevations.” These words are 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 New Mexico: Background for Survey, by D. E. Stuart and R. 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.

Let p₁ be the population proportion of unidentifi­ed archaeological artifacts at the elevation zone 7000–7500 feet in the given archaeological area. Let p₂ be the population proportion of unidenti­fied archaeological artifacts at the elevation zone 5000–5500 feet in the given archaeological area.

(a) Check Requirements Can a normal distribution be used to approximate the ₁ – ­₂ distribution? Explain.

(b) Find a 99% con­fidence interval for p₁ – p₂.

(c) Interpretation Explain the meaning of the confi­dence interval 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 comparison of the population proportion of unidenti­fied artifacts at high elevations (7000–7500 feet) with the population proportion of unidenti­fied artifacts at lower elevations (5000–5500 feet)? How does this relate to the stated hypothesis?

Transcribed Image Text:

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