Confidence Intervals (Shells) Homework

Name _____________________

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GEO 370 Numerical Methods in Geography Confidence Intervals (Shells) Homework

Background

Shell middens are deposits of old mollusk shells, left as trash by the prehistoric people who consumed mollusks (clams, oysters, etc.) as an important food source. The seashells are very slow to weather in many natural environments, and their lingering presence is an indication that prehistoric people once gathered and ate at that location. Such tribes were often nomadic, so they did not leave behind permanent housing structures to indicate that they resided at the area. The shell middens can help confirm the past presence of these peoples.

A statistical application in archaeology

A small archaeological team discovers a location in interior Baja California where there are shell middens. A research paper in a respected archaeological journal suggests that major settlements exist where at least 150,000 shell deposits remain. The archaeological team seeks to know whether the location they have discovered was once a major settlement.

During preliminary reconnaissance, the team splits up and finds that the shells are scattered over a 2 km2 area. The team only contains four people, and they are unable to completely scour the entire site to count shells and their fragments. So they decide to try a statistical sampling approach.

Each person will sample 25 locations, organized by a 5 × 5 grid. Each sample location will be a 2 m × 2 m cell, and within this sample location, the archaeologist will meticulously count every mollusk shell found. The geographic coordinates of the grid center (the origin) will be assigned by using a random number table. When the researcher finishes counting in the first cell, he/she will advance to a next cell in the 25-member grid. The distance from one grid point (i.e., the center of the 2 m × 2 m cell) to another is 20 m. The layout is shown in the figure below.

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1. Using the terminology of the textbook, the sampling pattern would be described as what particular type of spatial or composite sampling? (2 pts.)

2. What is the total area of the study domain? Please state your answer in hectares (1 ha=10,000 m2). (2 pts.)

3. Given the 4 m2 coverage per sample, what is the theoretical maximum number of samples which could be obtained? That is, assuming abundant labor, what would be the population size for the 2 km2 location? (3 pts.)

4. Considering the number of samples collected, compute the finite population correction factor. Comment on whether the finite population correction factor is a necessary consideration for this study. (3 pts.)

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5. What is the total number of shells on the site, computed to 90 percent certainty? Be sure to express your answer as a range. (8 pts.)

6. Was the site a major Native American settlement? Please write your answer in a full sentence, citing your evidence. (1 pt.)