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 x̄ = 74.6 and s = 9.8 on breaking strength (MPa). Estimate the true mean breaking strength of the white wood with a 95% confidence interval. Interpret the result.

Find the 95% confidence interval for the true mean breaking strength of the white wood.

(___,___) (round to 2 decimal places)

Answer 1

Solution :

Given that,

= 74.6

s = 9.8

n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,15 = 2.131

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

= 2.131 * (9.8 / 16)

= 5.22

The 95% confidence interval estimate of the population mean is,

- E < < + E

74.6 - 5.22 < < 74.6 + 5.22

69.38 < < 79.82

(69.38 , 79.82)