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.

1278

1243

1278

1306

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 =

S=

(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
upper limit

Answer 1

a)

x = 1284
s = 24

b)

sample mean, xbar = 1284
sample standard deviation, s = 24
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 * 24/sqrt(9)
ME = 14.88

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1284 - 1.86 * 24/sqrt(9) , 1284 + 1.86 * 24/sqrt(9))
CI = (1269 , 1299)

lower limit = 1269
Upper limit = 1299