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.

1194

1292

1285

1292

1268

1316

1275

1317

1275

(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:

Given: The method of tree ring dating gave the following years A.D. for an archaeological excavation site.

1194

1292

1285

1292

1268

1316

1275

1317

1275

We have to find  a 90% confidence interval for the mean of all tree ring dates from this archaeological site.

Formula:

where

Thus we need to make following table:

x	x2
1194	1425636
1292	1669264
1285	1651225
1292	1669264
1268	1607824
1316	1731856
1275	1625625
1317	1734489
1275	1625625

Thus

and

Now find t critical value:

df = n- 1 = 9 - 1 = 8

Two tail area = 1 - c = 1 - 0.90 = 0.10

Look in t table for df = 8 and two tail area = 0.10

t_c = 1.860

Thus

Thus

Thus

Lower Limit = 1257 AD
Upper Limit = 1302 AD