Chapter 10, Problem 1CS

CASE STUDY How Old Is Stonehenge?

Approximately eight miles north of Salisbury, Wiltshire, England, stands a large prehistoric circular stone monument surrounded by an earthwork, called Stonehenge. The monument consists of an outer ring of sarsen stones, surrounding two inner circles of bluestones. The entire structure is surrounded by a ditch and bank with 56 pits named the Aubrey Holes, after their discoverer, that appear to have been filled shortly after their excavation.

Corinn Dillion 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 the Stonehenge artifacts. The ratio of carbon-14 to carbon-12 remains constant in living organisms. Once the organism dies, the amount of carbon-14 in the remains begins to decline, because it is radioactive, with a half-life of 5730 years (the “Cambridge half-life”). The decay of carbon-14 into ordinary nitrogen makes possible a reliable estimate about the time of death of the organism. The counted carbon-14 decay events can be modeled by the normal distribution.

Stonehenge’s main ditch was dug in a series of segments. Excavations at the base of the ditch uncovered antlers bearing signs of heavy use, possibly used by the builders as picks or rakes and buried in the ditch shortly after its completion. Another researcher, Phillip Corbin had previously claimed that the mean date for the construction of the ditch was 2950 B.C. A sample of nine age estimates from unshed antlers excavated from the ditch produced a mean of 3033.1 B.C., with standard deviation 66.9 years. Assume that the ages are normally distributed with no outliers. At an α = 0.05 significance level, is there any reason to dispute Corbin’s claim?

Four animal bone samples were discovered in the ditch terminals, bearing signs of attempts at artificial preservation and possibility of 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 outliers. Use an α = 0.05 significance level to test the hypothesis 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. Excavation here revealed an antler, an antler tine, and an animal bone. Each artifact was submitted for dating and 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 outliers. Use an α = 0.05 significance level to test the hypothesis that the population mean age of the 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, part of a formation of concentric circles. 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 outliers. Use an α = 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 Corinn Dillion detailing your analysis.