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

Solution:

Part a

The mean and standard deviation for the given data are given as below:

Xbar = 74.2

S = 18.3

Part b

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 74.2

S = 18.3

n = 15

df = n – 1 = 14

Confidence level = 85%

Critical value by using t-table = 1.5231

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 74.2 ± 1.5231*18.3/sqrt(15)

Confidence interval = 74.2 ± 1.5231*4.725039682

Confidence interval = 74.2 ± 7.1967

Lower limit = 74.2 - 7.1967 = 67.0 cm

Upper limit = 74.2 + 7.1967 = 81.4 cm

Confidence interval = (67.0, 81.4)

lower limit	67.0 cm
upper limit	81.4 cm