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. 1,194 1,313 1,229 1,250 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.) tc = 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

Let   be the ith year A.D for an archaeological excavation site.

(a) Mean:  

Standard deviation:

(b) Here we use one sample t-test

degrees of freedom= n-1 = 9-1 =8

Critical value:

Critical value for 90% confidence level is 1.860

(c) Maximal margin of error

The maximal margin of error when finding 90% confidence interval for the mean of all tree ring dates from this archaeological site is 26

(d) 90% confidence interval for the mean of all tree ring dates from this archaeological site:

Lower limit = 1245 A.D.  

Upper limit = 1297 A.D.