Answer to Question #240683 in Statistics and Probability for Marie

Question

An article in the Journal of Composite Materials (December 1989, Vol. 23, p. 1200) describes the effect of delamination on the natural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies (in hertz) were as follows: 230.66 233.05 232.58 229.48 232.58 Calculate a 99% two-sided confidence interval on mean natural frequency.

Answer 1

n=5

Mean

$\bar{x} = \frac{(230.66+ 233.05+ 232.58,+229.48+232.58) }{ 5} =231.67$

$\sum (x_i- \bar{x})^2 = 9.3768 \\ s = \sqrt{ \frac{\sum(x_i- \bar{x})^2}{n-1}} = \sqrt{\frac{9.3768}{5-1}} = 1.5311 \\ α=0.01 \\ t_{α/2, n-1} = t_{0.01/2, 4} = 4.604$

Two-sided confidence interval:

$CI = (\bar{x} - \frac{t_{tab} \times s}{\sqrt{n}}, M + \frac{t_{tab} \times s}{\sqrt{n}}) \\ CI = (231.67 - \frac{4.604 \times 1.5311}{\sqrt{5}}, 231.67 + \frac{4.604 \times 1.5311}{\sqrt{5}}) \\ CI = (231.67 -3.152, 231.67 + 3.152) \\ CI = (228.518, 234.822)$