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.

1229

1257

1264

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.)

mean = A.D

Standard Deviation = . 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 =  

upper limit =

Answer 1

Solution :

Given that 1229   1257   1264   1194   1268   1316   1275   1317   1275

(a) => mean x = 1266 A.D

=> Standard deviation s = 39 yr

Mean :
=> sum of terms = 1229 + 1257 + 1264 + 1194 + 1268 + 1316 + 1275 + 1317 + 1275 = 11395

=> number of terms = 9

=> Mean = sum of terms/number of terms

= 11395/9

= 1266.1111

= 1266 (nearest whole number)

standard deviation :

=> standard deviation s = 38.576  

= 39 (nearest whole number)

(b) => Lower limit = 1242

   => Upper limit = 1290

Explanation :

=> n = 9 , df = n - 1 = 8

=> For 90% confidence interval , t = 1.860

=> The 90% confidence interval of the mean is

=> x +/- t*s/sqrt(n)

=> 1266 +/- 1.860*39/sqrt(9)

=> (1241.82 , 1290.18)

=> (1242 , 1290) (nearest whole number)