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.

1243 1271 1271 1320 1268 1317 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.

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site.

Lower limit

Upper limit

Answer 1

a)

sample mean, xbar = 1284.11
sample standard deviation, s = 27.182

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 * 27.182/sqrt(9)
ME = 16.853

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1284.11 - 1.86 * 27.182/sqrt(9) , 1284.11 + 1.86 * 27.182/sqrt(9))
CI = (1267.26 , 1300.96)

Lower limit = 1267.26

Upper limit = 1300.96