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. Assume that the population of x values has an approximately normal distribution. 1292 1278 1264 1229 1268 1316 1275 1317 1275

x bar=

S=

b.) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round answers to nearest whole number)

lower limit=

upper limit=

Answer 1

sample mean, xbar = 1279.33
sample standard deviation, s = 27.0647
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 * 27.0647/sqrt(9)
ME = 16.78

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1279.33 - 1.86 * 27.0647/sqrt(9) , 1279.33 + 1.86 * 27.0647/sqrt(9))
CI = (1263 , 1296)

Lower limit = 1263
Upper limit = 1296