Question

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.

1292

1180

1208

1236

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 1

(A) We know that mean = (sum of all observations)/(number of observations)

setting the values, we get

Mean = (1292+1180+1208+1236+1268+1316+1275+1317+1275)/9 = 11367/9 = 1263

Formula for standard deviation is given as

where xi are given observation and x(bar) is mean = 1263, n is sample size = 9

setting the values, we get

this gives

rounding to nearest whole number, we get s = 47 years

(B) we have to find 90% confidence interval

we have mean x(bar) = 1263, s = 47 and n = 9

degree of freedom = n-1= 9-1 = 8

using t distribution table, we get t critical value = 1.860

Using the confidence interval formula

setting the given values, we get

this gives us

or

rounding to nearest whole numbers, we get

90% confidence interval range between 1234 A.D. to 1292 A.D.