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

1194

1201

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.)

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)

Mean :

= 11262 / 9 = 1251.33

Standard Deviation:

= √( (1/9-1) * (1222-1251.33333)2+(1194-1251.33333)2+(1201-1251.33333)2+(1194-1251.33333)2+(1268-1251.33333)2+(1316-1251.33333)2+(1275-1251.33333)2+(1317-1251.33333)2+(1275-1251.33333)2)

= √( (1/8) * (-29.333332 + -57.333332 + -50.333332 + -57.333332 + 16.666672 + 64.666672 + 23.666672 + 65.666672 + 23.666672))

= √( (1/8) * (860.444248889 + 3287.11072889 + 2533.44410889 + 3287.11072889 + 277.777888889 + 4181.77820889 + 560.111268889 + 4312.11154889 + 560.111268889))

= √ 2482.4997336

σ= 49.82469

(b) Confidence Interval