SOLUTION: The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

Question 1110626: The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1306 1215 1299 1215 1268 1316 1275 1317 1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)
x =
A.D.
s =
yr
(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)
lower limit
A.D.
upper limit
A.D.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(a) x = 1276 and standard deviation is 39
:
(b) 90% confidence interval
alpha(a) = 1 - (90/100) = 0.10
critical probability(p*) = 1 - (a/2) = 0.95
:
since the sample size is small(sample size < 30) and the population is normally distributed, we use the student t-tables
:
degrees of freedom(df) = 9 - 1 = 8
:
from the student t-tables, we see that a df=8 and p*=0.95 has a critical value(t-statistic) of 1.86
:
we do not have the population standard deviation, so we use the standard error
:
standard error(se) = sample standard deviation/square root(sample size)
se = 39/square root(9) = 13
:
margin of error(me) is cv * se
:
me = 1.86 * 13 = 24.18 is approximately 24
:
90% confidence interval is 1276 + or - 24
:
********************
lower limit is 1252
upper limit is 1300
********************
:

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