The white wood material used for the roof of an ancient temple is imported from
ID: 3219636 • Letter: T
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 bar x = 74.4 and s = 11.3 on breaking strength (MPa). Estimate the true mean breaking strength of the white wood with a 99% confidence interval. Find the 99% confidence interval for the true mean breaking strength of the white wood. (____, ____) (Round to two decimal places as needed.) Interpret this confidence interval. Choose the correct answer below. A. The architects are confident that 99% of the white wood is described by this interval. B. The architects can be 99.5% confident that the mean breaking strength of the white wood is outside this interval. c. The architects can be 99% confident that the mean breaking strength of the white wood is within this interval. D. The architects can be 99.5% confident that the mean breaking strength of the white wood is 74.4. E. The architects can be 1% confident that the mean breaking strength of the white wood is within this interval.Explanation / Answer
Solution:
We don’t know the population standard deviation so we use a t-based confidence
interval. The formula for the interval is x ±t/2s/n.
We have = 0.01 and n1 = 15 degrees
of freedom, so t/2 = t0.005 = 2.947.
The 90% confidence interval is = 74.4 ± 2.947 · 11.3/16
=74.5 ± 8.325
= (66.175, 82.825)
C. The architects can be 99.5% confident that the mean breaking strength of the white wood is within this interval.
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