Question

The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1229

1264

1292

1222

1268

1316

1275

1317

1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x =	A.D.
s =	yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit	A.D.
upper limit	A.D.

Answer 1

Solution:

Part a

Sample mean = Xbar = 1273

Sample standard deviation = S = 33

(by using calculator or excel)

Part b

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data,

We have

Xbar = 1273.111111

S = 33.16038466

n = 9

df = n – 1 = 8

Confidence level = 90%

Critical t value = 1.8595

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 1273.111111 ± 1.8595*33.16038466/sqrt(9)

Confidence interval = 1273.111111 ± 1.8595*11.05346155

Confidence interval = 1273.111111 ± 20.5544

Lower limit = 1273.111111 - 20.5544 = 1252.56

Upper limit = 1273.111111 + 20.5544 = 1293.67

Lower limit = 1253 A.D.

Upper limit = 1294 A.D.