16.1. The mean thickness of a plate girder used in a suspension bridge needs to

Question

16.1. The mean thickness of a plate girder used in a suspension bridge needs to be estimated using ultra- sonic testing. The mean thickness can be assumed to have a normal probability distribution with a mean (1) and standard deviation (). The standard deviation () is known to be 1.8 mm. The construction drawings indicate a mean thickness of 15 mm and a standard deviation of 2.0 mm. A sample of n = 20 was collected. The sample resulted in a mean of 16 mm. Determine: (a) the pos- terior mean thickness, (b) the posterior standard deviation, and (c) the 95% confidence intervals for thickness based on prior and posterior information.

Explanation / Answer

Solution:

a. The posterior mean thickness is the sample mean, X-bar = 16mm.

b. The posterior standard deviation is the standard error of the mean, Se = /n = 1.8/20 = 0.4025

c. 95% confidence interval is given by:-

X-bar ± t (a/2, n - 1)*/n

16 ± t (0.05/2, 20 - 1)*0.4025

16 ± 2.433*0.4025

16 ± 0.9794

15.0206, 16.9794

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