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.

1,229

1,292

1,264

1,201

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) When finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to three decimal places.)

t_c =________

What is the maximal margin of error when finding a 90% confidence interval for the mean of all tree-ring dates from this archaeological site? (Round your answer to the nearest whole number.)

E =________

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)

From the given data we get-

Sample mean x bar = 1271 AD , Sample standard deviation s = 38 yrs

b)

C = 0.90 so we get = 1 - C = 1 - 0.90 = 0.10 and n= 9

So for finding the critical value in excel, use the command =TINV(0.1, 8)

= 1.860

So we get Critical value t_c = 1.860

c)

the maximal margin of error when finding a 90% confidence interval E =  t_c * (s / sqrt(n))

= 1.860 * ( 38 / 3)

= 23

Hence the maximal margin of error when finding a 90% confidence interval for the mean of all tree-ring dates from this archaeological site is 23

90% confidence interval for the mean of all tree-ring dates from this archaeological site

lower limit = x bar - E = 1271 - 23   = 1247 A.D.

upper limit = x bar + E = 1271 + 23 = 1294 A.D.

Hope this will help you. Thank you :)