The industrial engineer evaluating logic wafers was also interested in the amoun
ID: 2960195 • Letter: T
Question
The industrial engineer evaluating logic wafers was also interested in the amount of silver required in the photographic stages. For the same 15 batches, the following net usages (grams per wafer) were determined:0.25 0.18 0.24 0.19 0.20
0.23 0.27 0.21 0.23 0.21
0.19 0.22 0.20 0.25 0.25
a. Construct a 95% confidence interval estimate of the mean silver usage per wafer.
b. Assuming that sample standard deviation actually is the population standard deviation, determine the required sample size for estimating the mean of the population (net silver usage per wafer) to be accurate within 0.02 grams for the confidence levels of:
90%
99.9%
Explanation / Answer
Given n=15, xbar=0.221, standard deviation= s = 0.027 (based on the data)
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a. Construct a 95% confidence interval estimate of the mean silver usage per wafer.
Given a=0.05, t(0.025, df=n-1=14)=2.14 (check student t table)
So 95% CI is
xbar ± t*s/n
--> 0.221 ± 2.14*0.027/sqrt(15)
--> ( 0.206, 0.236)
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b. Assuming that sample standard deviation actually is the population standard deviation, determine the required sample size for estimating the mean of the population (net silver usage per wafer) to be accurate within 0.02 grams for the confidence levels of:
90%
Given a=0.1, t(0.05, df=n-1=14)=1.76 (check student t table)
E=0.02
So n = (t*s/E)^2 = (1.76*0.027/0.02)^2 = 5.645376
Take n=6
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99.9%
Given a=0.001, t(0.0005, df=n-1=14)=4.14 (check student t table)
E=0.02
So n = (t*s/E)^2 = (4.14*0.027/0.02)^2 = 31.23692
Take n=32
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