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