Question

Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of prehistoric Indian ruins in the southwestern United States. Suppose it is thought that a certain pueblo was occupied around 1292 A.D. (based on evidence from potsherds and stone tools). The following data give tree-ring dates (A.D.) from adjacent archaeological sites:

1189

1267

1268

1275

1275

1271

1272

1316

1317

1230

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to one decimal place.)

x	=	A.D.
s	=	yr

(ii) Assuming the tree-ring dates in this excavation area follow a distribution that is approximately normal, does this information indicate that the population mean of tree-ring dates in the area is different from (either higher or lower than) 1292 A.D.? Use a 1% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 1292; H₁: μ ≠ 1292H₀: μ > 1292; H₁: μ = 1292    H₀: μ ≠ 1292; H₁: μ = 1292H₀: μ = 1292; H₁: μ < 1292H₀: μ = 1292; H₁: μ > 1292

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution and σ is unknown.The Student's t, since we assume that x has a normal distribution and σ is unknown.    The standard normal, since we assume that x has a normal distribution and σ is known.The Student's t, since we assume that x has a normal distribution and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the population mean of tree-ring dates in the area differs from 1292 A.D.There is insufficient evidence at the 0.01 level to conclude that the population mean of tree-ring dates in the area differs from 1292 A.D.    

Answer 1