Question

The white wood material used for the roof of an ancient temple is imported from a certain country. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at a university conducted a study to estimate the mean bending strength of the white wood roof. A sample of 16 pieces of the imported wood were tested and yielded the statistics x overbar equals 73.2 and s equals 10.7s breaking strength​ (MPa). Estimate the true mean breaking strength of the white wood with a 99% confidence interval. Interpret the result.

Find the 99% confidence interval for the true mean breaking strength of the white wood.

A.The architects can be 99.5 %confident that the mean breaking strength of the white wood is outside this interval.

B.The architects can be 1​%confident that the mean breaking strength of the white wood is 73.2.

C.The architects can be 1​%confident that the mean breaking strength of the white wood is within this interval.

D.The architects are confident that 99% of the white wood is described by this interval.

E.The architects can be 99% confident that the mean breaking strength of the white wood is within this interval.

Answer 1

Solution:

Confidence interval for Population mean is given as below:

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

We are given

Xbar = 73.2

S = 10.7

n = 16

df = n – 1 = 16 – 1 = 15

Confidence interval = 99%

Critical t value = 2.9467

(by using t-table or excel)

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

Confidence interval = 73.2 ± 2.9467*10.7/sqrt(16)

Confidence interval = 73.2 ± 2.9467*2.675

Confidence interval = 73.2 ± 7.8825

Lower limit = 73.2 - 7.8825 = 65.3175

Upper limit = 73.2 + 7.8825 = 81.0825

Confidence interval = (65.32, 81.08)

Interpretation:

E. The architects can be 99% confident that the mean breaking strength of the white wood is within this interval.