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.

1299

1243

1320

1271

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:

x	x2
1299	1687401
1243	1545049
1320	1742400
1271	1615441
1268	1607824
1316	1731856
1275	1625625
1317	1734489
1275	1625625
---	---
x=11584	x2=14915710

The sample mean is

Mean   = (x / n) )

=1299+1243+1320+1271+1268+1316+1275+1317+1275 / 9

=11584 / 9

=1287.1111

Mean   = 1287

The sample standard is S

  S =  ( x² ) - (( x)² / n ) n -1

=(14915710-(11584)²9 /8)

=(14915710-14909895.1111 / 8)

=5814.8889 /8

=726.8611

=26.9604

Degrees of freedom = df = n - 1 = 9 - 1 = 8

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,8 =2.797  

Margin of error = E = t_/2,df * (s /n)

= 2.797 * (27 / 9)

= 17

Margin of error = 17

The 90% confidence interval estimate of the population mean is,

- E < < + E

1287 - 17 < < 1287 + 17

1270 < < 1304

Lower limit = 1270

Upper limit = 1304