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.

1,201

1,208

1,194

1,278

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)

When finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to three decimal places.)

t_c =

What is the maximal margin of error when finding a 90% confidence interval for the mean of all tree-ring dates from this archaeological site? (Round your answer to the nearest whole number.)

E =  

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

(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.)

The sample size is n = 9 . The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	1201	1442401
	1208	1459264
	1194	1425636
	1278	1633284
	1268	1607824
	1316	1731856
	1275	1625625
	1317	1734489
	1275	1625625
Sum =	11332	14286004

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

s = 47

(b)

When finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to three decimal places.)

For df =n - 1 = 9 - 1 = 8

and alpha = 0.1

t_c = 1.859

What is the maximal margin of error when finding a 90% confidence interval for the mean of all tree-ring dates from this archaeological site? (Round your answer to the nearest whole number.)

Margin of error , E

E = 29

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.)

Confidence interval = ( mean - E, mean + E )

Confidence interval = ( 1259 - 29 , 1259 + 29 )

Confidence interval = ( 1230, 1288 )

lower limit A.D. = 1230

upper limit A.D. = 1288