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. 1208 1215 1278 1187 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)

Sample mean = X / n = 11339 / 9 = 1260 (Rounded to nearest whole number)

sample standard deviation S = sqrt [ ( X² - n² ) / n-1 ]

= 46 (Rounded to nearest whole number)

b)

df= n - 1 = 9 - 1 = 8

t critical value at 0.10 significance level with 8 df = 1.860

90% confidence interval for is

- t * S / sqrt(n) < <   + t * S / sqrt(n)

1260 - 1.860 * 46 / sqrt(9) < < 1260 + 1.860 * 46 / sqrt(9)

1231 < < 1289

Lower limit = 1231

Upper limit = 1289