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

(b) Compute a 98% 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

Consider the random variable X

X : depth at which archaeological artifacts from the wind Mountain excavation site.

let   be the mean depth at which archaeological artifacts from the wind Mountain excavation site.

since population variance is unknown we used t distribution to find confidence interval for mean.

(1-alpha) 100% interval for mean depth at which archaeological artifacts from the wind Mountain excavation site is

alpha = level of significance = 0.02

X	(X-Xbar)^2
85	116.64
45	852.64
120	2097.64
80	33.64
75	0.64
55	368.64
65	84.64
60	201.64
65	84.64
95	432.64
90	249.64
70	17.64
75	0.64
65	84.64
68	38.44
1113	4664.4

from t-table

Hence 98% confidence interval is

= ( 61.8, 86.6).

Lower limit = 61.8 cm.

Upper limit = 86.6 cm.