A sample of 25 pieces of laminate used in the manufacture of circuit boards was

Question

A sample of 25 pieces of laminate used in the manufacture of circuit boards was selected, and the amount of warpage (in.) under particular conditions was determined for each piece, resulting in a sample mean warpage of 0.0639 and a sample standard deviation of 0.0063. (b) Calculate an interval for which you can have a high degree of confidence that at least 95% of all pieces of laminate result in amounts of warpage that are between the two limits of the interval. (Use a 99% tolerance interval. Round your answers to four decimal places.)

Explanation / Answer

given that,

n=25 pieces

xbar=0.0639

s=0.0063

alpha=0.01

t24,0.01=2.4322

test statistic,

t(n-1),alpha=(xbar-u)/(s/sqrt(n))

u=xbar-(s/sqrt(n))*t(n-1),alpha      or u=xbar+(s/sqrt(n))*t(n-1),alpha  

= 0.0639 -((0.0063/sqrt(25))*2.4322)                 or u =0.0639 +((0.0063/sqrt(25))*2.4322)

u= 0.06083543                                                         u=0.06696457

                       " 0.06083543 <u<0.06696457"

interval for which you can have a high degree of confidence that at least 95% of all pieces of laminate result in amounts of warpage that are between the two limits of the interval

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