PROBLEM: 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 17^th century were actually 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: theabsolute size of the site and thenumber of stone ceremonial platforms. The archaeologist has also reasoned that she can get into theissue 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

1. Using the variable "ceremonial structures', plot a histogram, run the descriptives and interpret the results (in excel)
2. Construct a frequency distribution table for the sites and periods then interpret.
3. Construct a 95% Confidence Interval for the variable "distance to coast (in km)" then interpret.
4. 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.
5. 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?
6. Is there a significant difference in the site size between the two periods?
7. Is there a significant difference in the ceremonial structures between the three different sites?