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.

1257

1320

1285

1194

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:

Given that,

x	x2
1257	1580049
1320	1742400
1285	1651225
1194	1425636
1268	1607824
1316	1731856
1275	1625625
1317	1734489
1275	1625625
x = 11507	x2 =14724729

a ) The sample mean is   

Mean   = (x / n )

= ( 1257+1320+1285+1194+1268+1316+1275+1317+1275 / 9 )

= 11507 / 9

= 1278.5556

Mean   = 1278.56

The sample standard is S

S = ( x² ) - (( x )² / n ) / 1 -n )

= ( 14724729 ( 11507 )² / 9 ) / 8

   = ( 14724729 -14712338.7778 / 8 )

= (12390.2222 / 8 )

= 1548.7778

= 39.3545

The sample standard is = 39.35

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

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,8 =1.860

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

= 1.860 * (39.35 / 9)

= 24.39

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

- E < < + E

1278.55 - 24.39 < < 1278.55 + 24.39

1254.16 < < 1302.94

Lower lilit = 1303

Upper limit = 1254