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Chapter 10: Project How Old is Stonehenge? This project is based on a similar project found on the Resource CD that was included with your textbook. Each section of your group's final report must be written clearly, paying attention to proper spelling and grammar 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 of bluestones. 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 are 56 pits, named the Aubrey Holes after their discoverer. These holes appear to have been filled shortly after their excavation. Recently, it has been discovered that a number of the stone alignments are associated with important solar and lunar risings and settings, suggesting that the site served as some sort of massive astronomical calendar. If this conclusion is accurate, it seems likely that the monument might have been used as a temple for sky worshipers. 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. Carbon-14 is one of three carbon isotopes found in Earth's atmosphere. 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 of the organism begins to decline, because it is radioactive, with a half-life of 5730 years (the "Cambridge half-life"). So 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. Dillion's team used two different carbon-14 dating methods to arrive at age estimates for the numerous Stonehenge artifacts. The liquid scintillation counting (LSC) method utilizes benzene, acetylene, ethanol, methanol, or a similar chemical. Unlike the LSC method, the accelerator mass spectrometry (AMS) technique offers direct carbon-14 isotope counting. The AMS method's greatest advantage is that it requires only milligram-sized samples for testing. The AMS method was used only on recovered artifacts that were of extremely small size. Source: This fictional account is based on information obtained from Archaeometry and Stonehenge (http://www.engh.gov.uk/stoneh/start.htm). The means and standard deviations used throughout this case study were constructed by calculating the statistics from the midpoint of the calibrated date range supplied for each artifact. Section 1 - Dating samples from the Stonehenge site 1. Stonehenge's main ditch was dug in a series of segments. Excavations at the base 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 fact that no primary silt was discovered beneath the antlers suggests that they were buried in the ditch shortly after its completion. Another researcher, Phillip Corbin, using an archeological markings approach, had previously claimed that the mean date for the construction of the ditch was 2950 BC. A sample of nine age estimates from unshed antlers excavated from the ditch produced a mean of 3033.1 BC, with standard deviation 66.9 years. Assume that the ages are normally distributed with no obvious outliers. At an = 0.05 significance level, is there any reason to dispute Corbin's claim? Answer: 3033.1-2950/66.9/57=9.378045464 P=3.415983 Critical Value:, Za/2=1.96 Z Interval: (3015.7, 3050.5) No, there is no reason to dispute Corbin's claim. Answer 2 = (3033.1-2950 )(66.9 / 9) 83.1/22.3 3.726 2. 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 BC and standard deviation of 67.4 years. Assume that the ages are normally distributed with no obvious outliers. Use an = 0.05 significance level to test the claim that the population mean age of the site is different from 2950 BC. Answer: 3187.5-2950/67.44= 7.047477745 P=9.170133 Critical Value: Z a/2=1.96 Z Interval: (3121.4, 3253.6) 3. 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 BC, with a standard deviation of 104.1 years. Assume that the ages are normally distributed with no obvious outliers. Use an = 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 BC. Answer: 2193.3-2950/104.1/3= -12.59022907 P=1 Critical Value Z a/2: 1.63 Z Interval: (2075.5, 2311.1) 4. 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 BC with a standard deviation of 99.7 years. Assume that the ages are normally distributed with no obvious outliers. Use an = 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 BC. Answer: 1671.7-2950/99.7/3= -22.21785133 P=1 Critical Value: 1.96 Z Interval: (1558.3, 1783.9) Section 2 - Interpreting the findings 5. 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 BC 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? (Remember: When you are working with BC dates, higher numbers are older.) Explain. Answer: The main ditch artifacts had a sample mean of 3033.1 BC which is older than the mean age 2950 BC which Corbin claims. The sample mean of the artifacts from the ditch terminals 3187.5 BC which is also older than the 2950 BC mean age which Corbin claims. The Bluestones had a sample mean of 2193.3 BC which is younger than 2950 BC mean age. The Y and Z holes sample mean of 1671.7 BC is also younger than 2950 BC mean age which Corbin claims. Construction order from oldest to newest: 1. Ditch terminals 2. Main ditch artifacts 3. The Bluestones 4. The Y and Z Holes 6. 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? (Remember: When you are working with BC dates, higher numbers are older.) Explain. Answer: The intervals below don't help Corbin's claim since the time frames are broad since the oldest interval begins at 3253.6 BC in the ditch terminal and the artifacts found in the Y and Z Holes have a range at 1558.3 BC. That is a difference of 1695.3 years between the two areas around Stonehenge where artifacts were found. Main Ditch: Z Interval: (3015.7, 3050.5) Ditch Terminal: Z Interval: (3121.4, 3253.6) Blue Stone: Z Interval: (2075.5, 2311.1) The Y and Z Holes: Z Interval: (1558.3, 1783.9) 7. Which statistical technique, hypothesis testing or confidence intervals, is more useful in assessing the age and likely construction order of the Stonehenge structures? Explain. Answer: Hypothesis testing has an issue of varying sample to sample. Confidence intervals lead to a wider interval and the interval is determined by the margin of error. The confidence interval gives a range of the artifact's age and the construction order of the Stonehenge structures. Confidence interval is the preferred choice since the hypothesis testing could vary in each sample and the construction order could be determined easier with confidence intervals. 8. Discuss the limitations and assumptions of your analysis. Is there any additional information that you would like to have before publishing your findings? Explain. Answer: The limitations and assumptions are based on the analysis is based on carbon dating which has been proven to be inaccurate is based upon \"assumptions\" instead of \"fact\". I would like to know about how fast certain animals decay, natural resources in the area, study on weather in that area, how far down were the items found in the ground, how much carbon dioxide was in the animal when it died, was there human bias, and the carbon dioxide in the air at the time of death of the animals. Write a report to Corinn Dillion detailing your analysis. Once your group has prepared a final report for this case study, one member of your group should submit the final report for grading. To do this, click the Dropbox link in the Course Navigation bar. In the Dropbox area, click the link for Project #3, and upload the saved file. Please refer to the Course Content for the due date of this project