Question

The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi. A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from present-day surface grade to the location of significant archaeological artifacts†.

85 45 120 80 75 55 65 60 65 95 90 70 75 65 68

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.) x = cm s = cm

(b) Compute a 85% confidence interval for the mean depth μ at which archaeological artifacts from the Wind Mountain excavation site can be found. (Round your answers to one decimal place.) lower limit cm upper limit cm

Answer 1

a)

x = 74.2

s = 18.3

b)
sample mean, xbar = 74.2
sample standard deviation, s = 18.3
sample size, n = 15
degrees of freedom, df = n - 1 = 14

Given CI level is 85%, hence α = 1 - 0.85 = 0.15
α/2 = 0.15/2 = 0.075, tc = t(α/2, df) = 1.523

ME = tc * s/sqrt(n)
ME = 1.523 * 18.3/sqrt(15)
ME = 7.196

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (74.2 - 1.523 * 18.3/sqrt(15) , 74.2 + 1.523 * 18.3/sqrt(15))
CI = (67 , 81.4)