Question

Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site.

1277 1126 1205 1228 1131 1209 1150 1174 1186

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

1157.6 to 1215.8

1157.1 to 1215.8

1158.9 to 1215.8

1157.1 to 1217.5

1158.9 to 1217.5

Answer 1

From the sample data,

= 1187.3333

S = 48.7134

t critical value at 0.10 level with 8 df = 1.86

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

1187.3333 - 1.86 * 48.7134 / sqrt(9) < < 1187.3333 + 1.86 * 48.7134 / sqrt(9)

1157.1 < < 1217.5

90% CI is ( 1157.1 , 1217.5)

Answer 2

From the sample data,

= 1187.3333

S = 48.7134

t critical value at 0.10 level with 8 df = 1.86

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

1187.3333 - 1.86 * 48.7134 / sqrt(9) < < 1187.3333 + 1.86 * 48.7134 / sqrt(9)

1157.1 < < 1217.5

90% CI is ( 1157.1 , 1217.5)