An archaeologist has conducted an archaeological surface survey
mikaiscute
Open question
2022-05-07
An archaeologist has conducted an archaeological surface survey in a region of western New Zealand consisting of a large and fertile valley with a major river flowing down to the coast. The archaeologist has hypothesized that the extremely complex Maori chiefdoms that the Europeans encountered upon contact in the 17th century were relatively recent developments in response to population pressure in the latest prehistoric phase. Further, she has argued that what was once a coastally focused chiefdom oriented towards a maritime economy, became increasingly inland-focused over time, with a subsistence emphasis on root crop agriculture rather than marine resource exploitation in the latest phase.
Sites appear on the surface as large quantities of subsistence debris and lithic artifacts (they had no ceramics), without standing architecture except for readily visible stone ceremonial platforms. The archaeologist has identified two major cultural phases in the region: (1) PHASE I (dated to about A.D. 1000-1300) and (2) PHASE II (dated to about A.D. 1300-1500) from 3 different sites. The archaeologist would like to examine the variable of “population size” in two ways: the absolute size of the site and the number of stone ceremonial platforms. The archaeologist has also reasoned that she can get into the issue of relative reliance on agriculture vs. maritime subsistence by looking at both the distance of sites from the coast and the relative density of fish bones, shell and other marine resources in the surface remains at the site before and after a long period of time. The data collected are as follows:
| Site | Period | Size (in ha.) | # Ceremonial Structures | Distance to Coast (in km) | % Marine Resources(before) | % Marine Resources(after) |
| 1 | 1 | 3.40 | 5.00 | 3.20 | 61.00 | 58.00 |
| 2 | 1 | 9.80 | 7.00 | 1.20 | 56.00 | 55.00 |
| 3 | 1 | 4.20 | 6.00 | 3.30 | 54.00 | 52.00 |
| 1 | 1 | 1.20 | 2.00 | 7.30 | 31.00 | 29.00 |
| 2 | 1 | 3.30 | 6.00 | 4.40 | 61.00 | 60.00 |
| 3 | 1 | 2.50 | 4.00 | 5.30 | 45.00 | 45.00 |
| 1 | 1 | 5.40 | 5.00 | 2.10 | 58.00 | 58.00 |
| 2 | 1 | 1.60 | 2.00 | 6.80 | 46.00 | 45.00 |
| 3 | 1 | 2.80 | 5.00 | 5.80 | 47.00 | 46.00 |
| 1 | 1 | 4.70 | 6.00 | 3.40 | 51.00 | 50.00 |
| 2 | 1 | 3.60 | 4.00 | 4.40 | 62.00 | 61.00 |
| 3 | 1 | 9.70 | 3.00 | 2.40 | 53.00 | 53.00 |
| 1 | 1 | 2.20 | 2.00 | 6.70 | 32.00 | 30.00 |
| 2 | 1 | 2.80 | 3.00 | 5.20 | 61.00 | 60.00 |
| 3 | 1 | 2.90 | 4.00 | 4.20 | 67.00 | 66.00 |
| 1 | 2 | 5.40 | 5.00 | 1.30 | 56.00 | 55.00 |
| 2 | 2 | 3.30 | 2.00 | 9.30 | 16.00 | 14.00 |
| 3 | 2 | 9.40 | 6.00 | 7.50 | 32.00 | 30.00 |
| 1 | 2 | 8.20 | 4.00 | 5.80 | 45.00 | 43.00 |
| 2 | 2 | 13.40 | 8.00 | 7.80 | 34.00 | 30.00 |
| 3 | 2 | 2.20 | 2.00 | 8.50 | 26.00 | 25.00 |
| 1 | 2 | 6.50 | 5.00 | 5.60 | 42.00 | 42.00 |
| 2 | 2 | 7.30 | 5.00 | 6.30 | 41.00 | 40.00 |
| 3 | 2 | 4.30 | 4.00 | 8.90 | 24.00 | 23.00 |
| 1 | 2 | 4.10 | 3.00 | 9.10 | 12.00 | 11.00 |
| 2 | 2 | 7.10 | 4.00 | 7.10 | 48.00 | 46.00 |
| 3 | 2 | 9.50 | 6.00 | 7.50 | 36.00 | 35.00 |
| 1 | 2 | 3.50 | 4.00 | 3.20 | 57.00 | 56.00 |
| 2 | 2 | 10.30 | 6.00 | 6.20 | 34.00 | 33.00 |
| 3 | 2 | 2.50 | 3.00 | 4.50 | 46.00 | 46.00 |
| 1 | 2 | 5.60 | 4.00 | 5.30 | 49.00 | 49.00 |
| 2 | 2 | 9.10 | 5.00 | 6.50 | 35.00 | 35.00 |
| 3 | 2 | 9.90 | 7.00 | 7.20 | 22.00 | 22.00 |
| 1 | 2 | 3.20 | 3.00 | 4.30 | 54.00 | 53.00 |
| 2 | 2 | 9.20 | 7.00 | 7.10 | 35.00 | 30.00 |
| 3 | 2 | 5.30 | 5.00 | 8.30 | 32.00 | 32.00 |
| 1 | 2 | 4.90 | 5.00 | 9.50 | 21.00 | 20.00 |
| 2 | 2 | 5.10 | 5.00 | 10.20 | 12.00 | 15.00 |
| 3 | 2 | 6.10 | 6.00 | 8.20 | 23.00 | 23.00 |
| 1 | 2 | 6.80 | 6.00 | 6.70 | 33.00 | 30.00 |
a. Using the variable “ceremonial structures’, plot a histogram, run the descriptive and interpret the results.
b. Construct a frequency distribution table for the sites and periods then interpret.
c. Construct a 95% Confidence Interval for the variable “distance to coast (in km)” then interpret.
d. Is there a reason to believe that the sample average site size (in ha) is the same as the population site size of 6 ha? Run the appropriate statistical tool and interpret.
e. The archaeologist suspects that the percentage of marine resources decreased after a long period of time. Is there a reason to believe in the archaeologist’s claim?
f. Is there a significant difference in the site size between the two periods?
g. Is there a significant difference in the ceremonial structures between the three different sites?
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b) Compute the probability that three or fewer passengers arrive in a one-minute period.
c) Compute the probability of no arrivals in a 15-second period.
d) Compute the probability of at least one arrival in a 15-second period.
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Given that a product was found to be defective, what is the probability that it was found by the first inspector?
(d)
Compute P(x ≥ 2).
P(x ≥ 2) =
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To test this, 20 items are randomly selected from the product.
If at most 3 items are defective, then the manufacturer is statement is accepted.
If the true probability of an item being defective is 0.2.
Find the probability of accepting the manufacturer’s statement?
(Hint: use the Binomial Distribution)
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Between what two times, in days, will a majority of babies arrive?
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(b) find the critical value
zα/2,
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