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 95% 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.)

Answer 1

Solution:

Sample mean = (85+45+120+80+75+55+65+60+65+95+90+70+75+65+68)/15 = 1113/15= 74.2

Sample standard deviation = sqrt(summation(Xi-mean)^2/(n-1) = sqrt((85-74.2)^2 +(45-74.2)^2+(120-74.2)^2+(80-74.2)^2+(75-74.2)^2+(55-74.2)^2+(65-74.2)^2+(60-74.2)^2+(65-74.2)^2+(95-74.2)^2+(90-74.2)^2+(70-74.2)^2+(75-74.2)^2+(65-74.2)^2+(68-74.2)^2)/14 = 17.63

95% confidence interval can be calculated as

Mean +/- talpha/2*sd/sqrt(n)

74.2+/- 2.14*17.63/sqrt(15)

74.2+/- 9.75

So 95% confidence interval is

64.5to 83.9