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 75.7 and s equals 10.9 on breaking strength (MPa). Estimate the true mean breaking strength of the white wood with a 95 % confidence interval. Interpret the result.

The architects can be 95% confident that the mean breaking strength of the white wood is within this interval (149.736 , 1.664)

Step-by-step explanation:

Given

Sample = n = 16

x = 75.7

s = 10.9

First we Calculate the degree of freedom.

Degree of freedom is calculated as

df = (n - 1)t

df = (16 - 1)t

df = 15t

The we check the t-table corresponding value for 0.05

t 0.05= 1.75377.

0.05 is gotten from

(100% - 95%) = 5%= 5/100 = 0.05

Calculating the True mean breaking strength through the confidence interval

Solving the confidence interval.

This is given by:

x ± ts√df

Confidence Interval = 75.7 ± 1.75377 * 10.9 * √15

Confidence Interval = 75.7 ± 74.036

Confidence Interval = 75.7 + 74.036 , 75.7 - 74.036

Confidence interval = 149.736 , 1.664

Interpreting the above;

The architects can be 95% confident that the mean breaking strength of the white wood is within this interval (149.736 , 1.664)