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.

1313

1194

1278

1187

1268

1316

1275

1317

1275

(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:

x	x2
1313	1723969
1194	1425636
1278	1633284
1187	1408969
1268	1607824
1316	1731856
1275	1625625
1317	1734489
x=10148	x2=12891652

a ) The sample mean is

Mean   = (x / n) )

= (1313+1194+1278+1187+1268+1316+1275+1317/ 9 )

= 10148 / 9

= 1127.5556

Mean   = 1127.56

The sample standard is S

  S = ( x² ) - (( x)² / n ) n -1

= (12891652 ( (10148 )² / 9 ) 8

   = (12891652 - 11442433.7778 / 8)

= (1449218.2222 / 8 )

= 181152.2778

= 425.6199

The sample standard is 425.62

b ) Degrees of freedom = df = n - 1 = 9 - 1 = 8

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,8 = 1.859  

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

= 1.859 * (425.62 / 9)

= 263.74

Margin of error = 263.74

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

- E < < + E

1127.56 - 263.74 < < 1127.56 + 263.74

863.82 < < 1391.30

(863.82, 1391.30 )