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. 1222 1180 1264 1208 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

Part a)

	Values ( X )	Σ ( Xi- X̅ )2
	1222	1296
	1180	6084
	1264	36
	1208	2500
	1268	100
	1316	3364
	1275	289
	1317	3481
	1275	289
Total	11325	17439

Mean X̅ = Σ Xi / n
X̅ = 11325 / 9 = 1258
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 17439 / 9 -1 ) = 47

Part b)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.1 /2, 9- 1 ) = 1.86
1258 ± t(0.1/2, 9 -1) * 47/√(9)
Lower Limit = 1258 - t(0.1/2, 9 -1) 47/√(9)
Lower Limit = 1229
Upper Limit = 1258 + t(0.1/2, 9 -1) 47/√(9)
Upper Limit = 1287
90% Confidence interval is ( 1229 , 1287 )