Solved: A manufacturer of semiconductor devices takes a
Chapter 9, Problem 144SE(choose chapter or problem)
A manufacturer of semiconductor devices takes a random sample of size of chips and tests them, classifying each chip as defective or nondefective. Let \(X_{i}=0\) if the chip is nondefective and \(X_{i}=1\) if the chip is defective. The sample fraction defective is
\(\hat{p}=\frac{X_{1}+X_{2}+\ldots+X_{n}}{n}\)
What are the sampling distribution, the sample mean, and sample variance estimates of \(\hat{p}\) when
(a) The sample size is \(n=50\)?
(b) The sample size is \(n=80\)?
(c) The sample size is \(n=100\)?
(d) Compare your answers to parts (a)-(c) and comment on the effect of sample size on the variance of the sampling distribution.
Equation Transcription:
Text Transcription:
X_i=0
X_i=1
p hat=X_1+X_2+ ... + X_n over n
p hat
n=50
n=80
n=100
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