Approximately 8 miles north of Salisbury, Wiltshire, England, stands a large circular stone monument

Approximately 8 miles north of Salisbury, Wiltshire, England, stands a large circular stone monument surrounded by an earthwork. This prehistoric structure is
known throughout the world as Stonehenge. Its name is derived from the Old
English word hengen, referring to something hung up. In the case of the monument, this name refers to the large horizontal lintel stones. The monument consists of an outer ring of sarsen stones, surrounding two inner circles ofbluestones. The first and third circles are adorned with the familiar stone lintels.The entire structure is surrounded by a ditch and bank. Just inside the bank are56 pits, named the Aubrey Holes, after their discoverer. These holes appear tohave been filled shortly after their excavation.

Recently, it has been discovered that a number of the stone alignments areassociated with important solar and lunar risings and settings, suggesting thatthe site served as some sort of massive astronomical calendar. If this conclusionis accurate, it seems likely that the monument might have been used as a templefor sky worshipers.

CorinnDillion is interested in dating the construction of the structure. Excavations at the site uncovered a number of unshed antlers, antler tines, and animal bones. Carbon 14 dating methods were used to estimate the ages of theStonehenge artifacts. Carbon 14 is one of three carbon isotopes found in Earth’satmosphere. Carbon 12 makes up 99% of all the carbon dioxide in the air. Virtually all the remaining 1% is composed of carbon 13. By far, the rarest form of
carbon isotope found in the atmosphere is carbon 14.

The ratio of carbon 14 to carbon 12 remains constant in living organisms.However, once the organism dies, the amount of carbon-14 in the remains ofthe organism begins to decline, because it is radioactive, with a half-life of5730 years (the “Cambridge half-life”). So the decay of carbon-14 into ordinary nitrogen makes possible a reliable estimate about the time of death ofthe organism. The counted carbon 14 decay events can be modeled by thenormal distribution.

Dillion’s team used two different carbon 14 dating methods to arrive at ageestimates for the numerous Stonehenge artifacts. The liquid scintillation counting (LSC) method utilizes benzene, acetylene, ethanol, methanol, or a similarchemical. Unlike the LSC method, the accelerator mass spectrometry (AMS)technique offers direct carbon 14 isotope counting. The AMS method’s greatestadvantage is that it requires only milligram-sized samples for testing. The AMSmethod was used only on recovered artifacts that were of extremely small size.

Stonehenge’s main ditch was dug in a series of segments. Excavations at thebase of the ditch uncovered a number of antlers, which bore signs of heavy use.These antlers could have been used by the builders as picks or rakes. The factthat no primary silt was discovered beneath the antlers suggests that they wereburied in the ditch shortly after its completion. Another researcher, PhillipCorbin, using an archeological markings approach, had previously claimed thatthe mean date for the construction of the ditch was 2950 B.C. A sample of nineage estimates from unshed antlers excavated from the ditch produced a mean of3033.1 B.C., with standard deviation 66.9 years. Assume that the ages are normally distributed with no obvious outliers. At an a = 0.05 significance level, isthere any reason to dispute Corbin’s claim?

Four animal bone samples were discovered in the ditch terminals. These
bones bore signs of attempts at artificial preservation and might have been in
use for a substantial period of time before being placed at Stonehenge. When
dated, these bones had a mean age of 3187.5 B.C. and standard deviation of 67.4
years. Assume that the ages are normally distributed with no obvious outliers.
Use an a = 0.05 significance level to test the claim that the population mean
age of the site is different from 2950 B.C.

In the center of the monument are two concentric circles of igneous rock
pillars, called bluestones. The construction of these circles was never completed.
These circles are known as the Bluestone Circle and the Bluestone Horseshoe.
The stones in these two formations were transported to the site from the Prescelly Mountains in Pembrokeshire, southwest Wales. Excavation at the center of
the monument revealed an antler, an antler tine, and an animal bone. Each artifact was submitted for dating. It was determined that this sample of three artifacts had a mean age of 2193.3 B.C, with a standard deviation of 104.1 years.
Assume that the ages are normally distributed with no obvious outliers. Use an
a = 0.05 significance level to test the claim that the population mean age of the
Bluestone formations is different from Corbin’s declared mean age of the ditch,
that is, 2950 B.C.

Finally, three additional antler samples were uncovered at the Y and Z
holes. These holes are part of a formation of concentric circles, 11 meters and 3.7
meters, respectively, outside of the Sarsen Circle. The sample mean age of these
antlers is 1671.7 B.C. with a standard deviation of 99.7 years. Assume that the
ages are normally distributed with no obvious outliers. Use an a = 0.05 significance level to test whether the population mean age of the Y and Z holes is different from Corbin’s stated mean age of the ditch, that is, 2950 B.C.

From your analysis, does it appear that the mean ages of the artifacts from
the ditch, the ditch terminals, the Bluestones, and the Y and Z holes dated by
Dillion are consistent with Corbin’s claimed mean age of 2950 B.C. for construction of the ditch? Can you use the results from your hypothesis tests to infer the
likely construction order of the various Stonehenge structures? Explain.

Using Dillion’s data, construct a 95% confidence interval for the population mean ages of the various sites. Do these confidence intervals support
Corbin’s claim? Can you use these confidence intervals to infer the likely construction order of the various Stonehenge structures? Explain.

Which statistical technique, hypothesis testing or confidence intervals, is
more useful in assessing the age and likely construction order of the Stonehenge structures? Explain.

Discuss the limitations and assumptions of your analysis. Is there any additional information that you would like to have before publishing your findings?
Would another statistical procedure be more useful in analyzing these data? If
so, which one? Explain. Write a report to CorinnDillion detailing your analysis.