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.

1250 1299 1306 1278 1268 1316 1275 1317 1275

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=

upper limit=

Answer 1

Solution:

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

From given data, we have

Xbar = 1287.111111

S = 23.30474439

n = 9

df = n – 1 = 8

Confidence level = 90%

Critical t value = 1.8595

(by using t-table)

Confidence interval = 1287.111111 ± 1.8595*23.30474439/sqrt(9)

Confidence interval = 1287.111111 ± 1.8595* 7.76824813

Confidence interval = 1287.111111 ± 14.4454

Lower limit = 1287.111111 - 14.4454 = 1272.67

Upper limit = 1287.111111 + 14.4454 = 1301.56

Lower limit = 1273

Upper limit = 1302