An article in the Journal of Composite Materials Vol 23 1989

An article in the Journal of Composite Materials (Vol 23, 1989, 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 Hz):

230.66,    233.05,    232.58,    229.48,    232.58

(a) Find a 95% two-sided CI on mean natural frequency. Round your answers to 2 decimal places..
(b) Do the results of your calculations support the claim that mean natural frequency is 235 Hz?

(a)
(b)

Solution

a)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    231.67          
t(alpha/2) = critical t for the confidence interval =    2.776445105          
s = sample standard deviation =    1.531078052          
n = sample size =    5          
df = n - 1 =    4          
Thus,              
              
Lower bound =    229.7689155          
Upper bound =    233.5710845          
              
Thus, the confidence interval is              
              
(   229.7689155   ,   233.5710845   ) [ANSWER]

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b)

No, as 235 is out of our confidence interval. [ANSWER]