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

1229 1257 1243 1194 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.)

(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.)

Answer 1

A) Mean = 1264

Standard deviation = 37

B) CI ≈ (1241, 1287)

Explanation:

A) Mean = Σx/n

Σx = 1229 + 1257 + 1243 + 1194 + 1268 + 1316 + 1275 + 1317 + 1275

Σx = 11374

Mean(x¯) = 11374/9

Mean(x¯) ≈ 1264

Standard deviation = √(∑(x - x¯)²/(n)

From online calculator;

Standard deviation; s ≈ 37

B) Our distribution factor is; DF = n - 1 = 9 - 1 = 8

From t-table attached, our critical value at 90% Confidence interval is t = 1.86

Formula for confidence interval is;

CI = x¯ ± t(s/√n)

CI = 1264 ± 1.86(37/√9)

CI = 1264 ± 22.94

CI ≈ (1241, 1287)