Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

At Burnt Mesa Pueblo, the method of tree ring dating gave the following years A.

ID: 3156191 • Letter: A

Question

At Burnt Mesa Pueblo, the method of tree ring dating gave the following years A.D. for an archaeological excavation site.

1189, 1271, 1267, 1272, 1268, 1316, 1275, 1317, 1275

a) Use the calculator with mean and standard deviation keys to verify that the sample mean year is 1272 with sample standard deviation 37 years.

b) Find 90% confidence interval for the mean of all three ring dates from this archaeological site.

c) What is the margin of error for the 90% confidence interval?

PLEASE SHOW CALCULATOR STEPS.

Explanation / Answer

a)

If you use a ti-84, construct a list L1, and the use 1-varstats to get the descriptive statistics (like mean and standard deviation). You will get

X = sample mean =    1272.222222   [ANSWER]
      
s = sample standard deviation =    36.9282337   [ANSWER]

******************************

b)      

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    1272.222222          

df = n - 1 =    8          

t(alpha/2) = critical t for the confidence interval =    1.859548038          

[In ti84, you can use invT(8, 1-0.05) to get this value.]

s = sample standard deviation =    36.9282337          
n = sample size =    9          
Thus,              
              
Lower bound =    1249.332281          
Upper bound =    1295.112164          
              
Thus, the confidence interval is              
              
(   1249.332281   ,   1295.112164   ) [ANSWER]

********************************

c)

Also,

Margin of error = t(alpha/2) * s / sqrt(n) = 22.8899415 [ANSWER]

********************************

Hi! If you use another calculator model, please resubmit this question indicating what calculator you use. That way we can continue helping you! Thanks!

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote