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.

1264

1208

1180

1306

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

Solution : Given that 1264 , 1208 , 1180 , 1306 , 1268 , 1316 , 1275 , 1317 , 1275

(a) Sum of terms = 1264 + 1208 + 1180 + 1306 + 1268 + 1316 + 1275 + 1317 + 1275 = 11409

Number of terms = 9

=> mean x = Sum of terms/Number of terms

= 11409/9

= 1268

=> standard deviation s = 47

(b) For 90% confidence interval , df = n-1 = 8 , t = 1.86

=> The 90% confidence interval for the mean is x +/- t*s/sqrt(n)

=> 1268 +/- 1.86*47/sqrt(9)

=> 1239 , 1297 (nearest whole munber)

=> lower limit 1239 A.D.

=> Upper limit 1297 A.D.