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.

1,243

1,292

1,187

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) 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

Solution :

We have

= 1264

s = 46

t _/2,df = 1.860

Margin of error = E = t_/2,df * (s /n)

= 1.860 * (46 / 9)

Margin of error = E = 29

The 90% confidence interval estimate of the population mean is,

- E < < + E

1264 - 29 < < 1264 + 29

12354 < < 1293

(1235 , 1293)

Lower limit = 1235 A.D.

Upper limit = 1293 A.D.