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.

1313

1257

1292

1215

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

Using TI-84 we can find mean and standard deviation.

Fist enter the values in TI-84.

Then follow the path :

STAT > CALC > 1-var stats> Enter

Hence we will get :

Mean = = 1281, Standard deviation = s = 33

b) The 90% confidence interval fo mean is given by

( - E, + E )

Where,

c = 0.90,

df = n-1 = 9-1 = 8

So,

= 20.46

Hence the required confidence interval is

( 1281 - 20.46, 1281 + 20.46 )

( 1260.54 , 1301.46 )

( 1261 , 1302 )

Lower limit = 1261 A.D.

Upper limit = 1302 A.D.