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.

1222

1208

1201

1250

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
1222	1493284
1208	1459264
1201	1442401
1250	1562500
1268	1607824
1316	1731856
1275	1625625
1317	1734489
1275	1625625
---	---
x=11332	x2=14282868

a ) The sample mean is

Mean = (x / n) )

=1222+1208+1201+1250+1268+1316+1275+1317+12759

=113329

=1259.1111

Mean = 1259

The sample standard is S

  S = ( x² ) - (( x)² / n ) n -1

=(14282868-(11332)² /9 )8

=(14282868-14268247.1111 / 8)

=14620.8889 /8

=1827.6111

=42.7506

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 * (42.75 / 9)

= 26.50

Margin of error =26.50

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

- E < < + E

1259 - 26.50< < 1259 + 26.50

1232.50 < < 1285.49

lower limit =1233

upper limit =1286