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 25 pieces of the imported wood were tested and yielded the statistics x=74.6 and s=9.9 on breaking strength​ (MPa). Estimate the true mean breaking strength of the white wood with a 90% confidence interval. Interpret the result.

Find the 90% confidence interval for the true mean breaking strength of the white wood.

Answer 1

Given that,

= 74.6

s =9.9

n = 25

Degrees of freedom = df = n - 1 =25 - 1 =24

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,24= 1.711 ( using student t table)

Margin of error = E = t_/2,df * (s /n)

= 1.711 * (9.9 / 25) = 3.3878

The 90% confidence interval estimate of the mean is,

- E < < + E

74.6- 3.3878 < < 74.6+ 3.3878

71.2122 < < 77.9878

(71.2122, 77.9878 )

The 90% confidence interval estimate of the mean is,(71.2122, 77.9878 )