Archaelogy: Tree Rings at Brunt Mesa Pueblo, archaeologicalstudies have used the

Question

Archaelogy: Tree Rings at Brunt Mesa Pueblo, archaeologicalstudies have used the method of tree ring dating in an effort todetermine when prehistoric people lived in the pueblo. Wood fromseveral excavations gave a mean of (year) 1243 with a standarddeviation of 36 years (Bandelier Archolological Excavation Project:Summer 1989 Excavations at Brunt Mesa Pueblo, edited by Kohler,Washington State University Department of Antropology). Thedistrubtition of dates was more or less mound shaped andsymmetrical about the mean. Use the empirical rule to: a. estimate a range of years centered about the mean in whichabout 68% of the data (tree ring dates) will be found. b. estimate a range of years centered about the mean in whichabout 95% of the data (tree ring dates) will be found. c. estimate a range of years centered about the mean in whichalmost all the data (tree ring dates) will be found. Archaelogy: Tree Rings at Brunt Mesa Pueblo, archaeologicalstudies have used the method of tree ring dating in an effort todetermine when prehistoric people lived in the pueblo. Wood fromseveral excavations gave a mean of (year) 1243 with a standarddeviation of 36 years (Bandelier Archolological Excavation Project:Summer 1989 Excavations at Brunt Mesa Pueblo, edited by Kohler,Washington State University Department of Antropology). Thedistrubtition of dates was more or less mound shaped andsymmetrical about the mean. Use the empirical rule to: a. estimate a range of years centered about the mean in whichabout 68% of the data (tree ring dates) will be found. b. estimate a range of years centered about the mean in whichabout 95% of the data (tree ring dates) will be found. c. estimate a range of years centered about the mean in whichalmost all the data (tree ring dates) will be found.

Explanation / Answer

Wood fromexcavations gave a mean of (year) 1243 with a standard deviation of36 years. The distribution of dates was more or less mound shapedand symmetrical about the mean. Use the empirical rule to:

a. estimatea range of years centered about the mean in which about 68% of thedata (tree ring dates) will befound.
     {Z Value For2-Tail 68% Range} = 0.9945
     {68%Range} =
          = {(1243) -(0.9945)*(36) < Y < (1243) +(0.9945)*(36) }
          = { 1207 < Y <  1279 }

b. estimatea range of years centered about the mean in which about 95% of thedata (tree ring dates) will be found.
     {Z Value For 2-Tail 95%Range} = 1.96
     {95%Range} =
          = {(1243) -(1.96)*(36) < Y < (1243) +(1.96)*(36) }
          = { 1172 < Y < 1314 }

c. estimatea range of years centered about the mean in which almost all thedata (tree ring dates) will befound.
     {Z Value For2-Tail 99% Range} = 3.0
     {99%Range} =
          = {(1243) -(3.0)*(36) < Y < (1243) + (3.0)*(36)}
          = { 1135 < Y < 1351 }

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