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.

1208

1208

1292

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

(a) mean is given by

Calculation

	x	(x-xbar)^2
	1208	3025
	1208	3025
	1292	841
	1208	3025
	1268	25
	1316	2809
	1275	144
	1317	2916
	1275	144
sum/ss	11367	15954
xbar	1263
s^2=ss/8		1994.25
s		44.65703

(b) 90% confidence interval for mean is

degrees of freedom = n-1 =8

For 95% confidence () with df =8 , two tailed critical value of t is

tc = 1.86 ( from t table)

Thus , 90% confidence interval for mean is

= (1235. 1, 1290.9 )

= ( 1235 , 1291)

lower limit = 1235

upper limit = 1291