Question

QUESTION # 1

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.

1,194

1,180

1,201

1,236

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.

QUESTION # 2

Use the Student's t distribution to find t_c for a 0.95 confidence level when the sample is 26.

Answer 1

Question 1

Part a

Xbar = 1,251

S = 51

Part b

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 1251

S = 51.27865053

n = 9

df = n – 1 = 8

Confidence level = 90%

Critical t value = 1.8595

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 1251 ± 1.8595*51.27865053/sqrt(9)

Confidence interval = 1251 ± 31.7850

Lower limit = 1251 - 31.7850 = 1219.55

Upper limit = 1251 + 31.7850 = 1283.12

Lower limit = 1220 A.D.

Upper limit = 1283 A.D.

Question 2

We are given

Confidence level = 95%

Sample size = n = 26

df = n – 1 = 25

So, critical value by using t table is given as below:

t_c = 2.0595