1. An industrial engineer for a nano-circuit manufacturer is estimating producti

Question

1.     An industrial engineer for a nano-circuit manufacturer is estimating production costs for a new logic chip. Hundreds of chips are produced on a single silicon sheet that is like a wafer cake with as many as 50 layers. The most expensive layers involve gold, which is applied in an aerosol mist. In order to estimate costs, the engineer needs data on the amount of gold that is consumed per wafer. A pilot run of 12 batches yields a sample mean of 0.18 ounce gold consumption per wafer with a sample variance of 0.0003. Conduct a test of hypotheses that the true mean gold consumption per wafer is at least 0.20 ounce. Use alpha = 0.01.

Conduct the test by using both the critical region method and by calculating a P-value.

Explanation / Answer

here null hypothesis: Ho: mean >=0.2

alternate hypothesis:Ha : mean <0.20

std error =(variance/n)1/2 where n=12

=0.005

for 0.01 level and (n-1=11) degree of freedom, value of tcritical =-2.718

test statistic t =(X-mean)/std error =(0.18-0.20)/0.005 =-4

as test stat t is less then t critical ; hence we reject null hypothesis.

also for above tstat , pvalue =0.001

as p value is lower then 0.01 level, we reject the null hypothesis.

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