1 The Wind Mountain archaeological site is located in southw

1) 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 80% confidence interval for the mean depth 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

2)

Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at an archaeological site. At one excavation, a sample of 177 potsherds indicated that 70 were of the three-circle, red-on-white pattern.

(a) Find a point estimate p for the proportion of all ceramic potsherds at this site that are of the three-circle, red-on- white pattern. (Round your answer to four decimal places.)

(b) Compute a 95% confidence interval for the population proportion p of all ceramic potsherds with this distinctive pattern found at the site. (Round your answers to three decimal places.)

lower limit

upper limit

Solution

1)

a)
Mean = 74.2  
Standard deviation = 18.25
b)
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=74.2
Standard deviation( sd )=18.25
Sample Size(n)=15
Confidence Interval = [ 74.2 ± t a/2 ( 18.25/ Sqrt ( 15) ) ]
= [ 74.2 - 1.345 * (4.71) , 74.2 + 1.345 * (4.71) ]
= [ 67.86,80.54 ]