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. 1,208 1,292 1,187 1,257 1,268 1,316 1,275 1,317 1,275 (

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

ANSWER:

Given that,

1,208

1,292

1,187

1,257

1,268

1,316

1,275

1,317

1,275

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.)

Sample mean year x = (1208+1292+1187+1257+1268+1316+1275+1317+1275) / 9

= 11395/9

= 1266.11

= 1266 A.D.

sample standard deviation s = sqrt(((1208-1266)^2+(1292-1266)^2+(1187-1266)^2+(1257-1266)^2+(1268-1266)^2+(1316-1266)^2+(1275-1266)^2+(1317-1266)^2+(1275-1266)^2) / (9-1))

= 44.19

= 44 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.)

c =90% = 90/100 = 0.90

= 1-c = 1-0.90 = 0.1

/2 = 0.1/2 = 0.05

Degree of freedom = df = n-1 = 9-1 = 8

Critical value = = = 1.859547

90% CI = Sample mean year x * (sample standard deviation s/sqrt(n))

90% CI = 1266 1.859547 * (44/sqrt(9))

90% CI = 1266 27.273356

90% CI = (1266-27.273356 , 1266+27.273356)

90% CI = (1238.726644 , 1293.273356)

90% CI = (1239 , 1293)

lower limit = 1239 A.D.

upper limit = 1293 A.D.

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