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.

1,180

1,250

1,208

1,180

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

Answer: n=9, C=90% = 0.90

a)

Using TI-83 calculator we calculate the mean and standard deviation for the given data.

We get values,

Sample mean = =1252.1111= 1252

Sample standard Deviation =S= 52.37710771= 52

b)

now formula for confidence interval is

     tc *  

Where tc is the t critical value with c= 0.90 and degree of freedom (df) = n-1 = 9-1 = 8

Using t table we can get t critical value

tc = 1.860

1252   1.860*

1219.8 < < 1284.2

(1220 , 1284)

lower limit =1220 A.D.

upper limit = 1284 A.D.