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.

1285

1194

1313

1264

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

	X	X2
	1285	1651225
	1194	1425636
	1313	1723969
	1264	1597696
	1268	1607824
	1316	1731856
	1275	1625625
	1317	1734489
	1275	1625625
Total	11507	14723945

Here

n = 9

The sample standard deviation is given by,

Critical value when population standard deviation is not known:

n = 9

degrees of freedom = n - 1 = 9 -1 =8

confidence level = 0.90.

Thus, the level of significance, α is 0.10 (= 1 – 0.90).

From student t - table,

Now, 90% confidence interval for the mean is,

( round to the nearest whole number)

So,

lower limit = 1255 AD

upper limit = 1302 AD