Question

A white wood used for the roof of an ancient Japanese temple was imported from Northern Europe. A study was conducted to test the mean bending strength of the white wood roof. A sample of 35 pieces of imported wood was tested for breaking strength (in MPa). The sample mean was 75.4 and a sample standard deviation was 10.9. Give a 90% confidence interval for the true mean breaking strength of the white wood.

Answer 1

Given that,

= 75.4

s =10.9

n = 35

Degrees of freedom = df = n - 1 =35 - 1 = 34

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,34 =1.691 ( using student t table)

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

= 1.691 * ( 10.9/ 35) = 3.12

The 90% confidence interval mean is,

- E < < + E

75.4 - 3.12< < 75.4+ 3.12

72.28 < < 78.52

(72.28 , 78.52 )