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

1313

1250

1299

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
1285	1651225
1313	1723969
1250	1562500
1299	1687401
1268	1607824
1316	1731856
1275	1625625
1317	1734489
1275	1625625
x=11598	x2=14950514

Mean = (x / n) )

a ) The sample mean is

Mean = (x / n) )=1285+1313+1250+1299+1268+1316+1275+1317+12759

=11598 /9
=1288.6667

Mean = 1289

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=(14950514-(11598)²9 /8)

=(14950514-14945956/8)

=4558/8

=569.75

=23.8694

The sample standard is =23.87

b ) 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 =1.859

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

= 1.859 * (23.87 / 9)

= 14.79

Margin of error =14.79

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

- E < < + E

1289- 14.79< < 1289 + 14.79

1274.20 < < 1303.79

lower limit =1274

upper limit =1304