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. 1201 1320 1215 1243 1268 1316 1275 1317

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x(with the bar above it) and sample standard deviation s. (Round your answers to the nearest whole number.)

x( with the bar on top) = ____ 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

Answer:-

A) sample mean =( 1201 +1320 +1215 +1243+ 1268 +1316+ 1275+ 1317 ) / 8 =10155 / 8 = 1269.375 =1269 (,nearest whole number

Sample standard deviation

s = 46.85 =47 (nearest whole number)

B)

90% confidence interval for mean is given as

Value of Z at 90 % confidence coefficient is 1.645

Therefore confidence interval is

= 1269.375 1.645*46.85

=( 1269.375 - 27.249 , 1269.375 + 27.249)

= ( 1252.13 , 1306.62) =(1252 ,1307) ~nearest whole number .

Hence, 90% confidence interval for the mean of all tree ring dates from this archaeological site is(1252.13 ,1306.62 )

Lower limit =1252.13 ~ 1252 (nearest whole number)

Upper limit= 1306.62 ~ 1307 (nearest whole number)