Semiconductor wafer and device process yields are some of the most closely guard
ID: 3128850 • Letter: S
Question
Semiconductor wafer and device process yields are some of the most closely guarded trade secrets in the semiconductor industry, and they measure how well a given semiconductor process can fabricate and package non-defective integrated circuits. Suppose a process used to manufacture CMOS chips produces the following sampling of process yields:
X = {68.5%, 77.2%, 78.6%, 74.3%, 75.4%, 77.4%, 48.6%, 69.7%, 72.7%, 76.2%}
Does the sample provided give any evidence that the mean yield is not 74%? Assume the standard deviation is 2.5%.
a) Findthemeanvalueofthesample.
b) Writeoutthedescriptionofthehypothesistestusingthestandardnotationand state whether it is one-sided or two-sided.
c) TestthehypothesisusingtheP-Valueapproach(hint:youneedtocomputethe z-standard value for the sample mean). What does the computed P-value suggest about the hypothesis?
d) Test the hypothesis using the fixed interval approach. Assume = 0.04. What is / are the z-values of the boundaries of the fixed interval? What does this test suggest about the hypothesis?
e) Suppose the true yield is actually 76%. What is the probability of a type II error under these circumstances? What is the power of this test? How many samples would you need to increase the power of the test to 95%?
f) Compute the 95% confidence intervals for the mean value of the sample. What do the confidence intervals suggest about the hypothesis?
Explanation / Answer
A)
Using technology to find the descriptive statistics,
X = sample mean = 71.86 [ANSWER]
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b)
Formulating the null and alternative hypotheses,
Ho: u = 74
Ha: u =/ 74
As we can see, this is a two tailed test. [ANSWER]
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c)
Getting the test statistic, as
X = sample mean = 71.86
uo = hypothesized mean = 74
n = sample size = 10
s = standard deviation = 2.5
Thus, z = (X - uo) * sqrt(n) / s = -2.706909677
Also, the p value is
p = 0.006791273 [P VALUE]
Hence, as P is very small, there is much evidence that the null hypothesis could be incorrect.
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d)
Thus, getting the critical z, as alpha = 0.04 ,
alpha/2 = 0.02
zcrit = +/- 2.053748911
As |z| > 2.0537, then there is significant evidence at 0.04 level that the the mean yield is not 74% at 0.04 level. [CONCLUSION]
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