Question

Background:

Excavations at Stonehenge 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 of the carbon dioxide in the air. Virtually all of 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.

The 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.

Question:

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 BCE and standard deviation of 67.4 years. Assume that the ages are normally distributed with no obvious outliers. Use an α = 0.05 significance level to test the claim that the population mean age of the site is different from 2950 BCE.

Answer 1