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.

1264

1208

1201

1285

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)

sample mean, xbar = 1268
sample standard deviation, s = 41

b)

sample size, n = 9
degrees of freedom, df = n - 1 = 8

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.86

ME = tc * s/sqrt(n)
ME = 1.86 * 41/sqrt(9)
ME = 25.42

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1268 - 1.86 * 41/sqrt(9) , 1268 + 1.86 * 41/sqrt(9))
CI = (1243 , 1293)

lower limit = 1243    A.D.
upper limit = 1293    A.D.