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 were as follows (in hertz):

230.66, 233.05, 232.58, 229.48, 232.58

Calculate a 95% two-sided confidence interval on mean natural frequency.

Answer 1

here

mean, = (230.66+ 233.05+ 232.58,+229.48+232.58) / 5 =231.67

std dev---

s = 1.53

To find a confidence interval, note that ¯ x = 231 . 67 , s = 1 . 53 , n = 5 and α = 0.05

so t _{α/ 2 ,n - 1} = t _{0 .025, 4} = 2.776. Thus a 95% two-sided confidence interval on the mean natural frequency is

- t_{α/ 2} ,_{n - 1} s √ n ≤ μ ≤   +t_{α/ 2} ,_{n - 1} s √ n

=231.67 - 2.776* 1 . 53 /√ 5 ≤ μ ≤ 231 . 67 + 2.776 *1 . 53 /√ 5

=229.771≤ μ≤233.570

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