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 1208 1215 1208 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
1208	1459264
1215	1476225
1208	1459264
1268	1607824
1316	1731856
1275	1625625
1317	1734489
1275	1625625
∑x=11381	∑x2=14407573

a ) Mean ˉx=∑xn

=1299+1208+1215+1208+1268+1316+1275+1317+12759

=113819

=1264.5556

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√14407573-(11381)298

=√14407573-14391906.77788

=√15666.22228

=√1958.2778

=44.2524

b ) Degrees of freedom = df = n - 1 = 9 - 1 = 824

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,8 =1.859

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

= 1.859 * (44 / 9)

= 27

Margin of error = 27

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

- E < < + E

1265 - 27 < < 1265+ 27

1238 < < 1292

lower limit A.D. =1238

upper limit A.D.=1292