An article reported that, in a study of a particular wafer inspection process, 3

Question

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 247 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question. The technology underlying hip replacements has changed as these operations have become more popular (over 250,000 in the United States in 2008). Starting in 2003, highly durable ceramic hips were marketed. Unfortunately, for too many patients the increased durability has been counterbalanced by an increased incidence of squeaking. An article reported that in one study of 150 individuals who received ceramic hips between 2003 and 2005, 9 of the hips developed squeaking. (a) Calculate a lower confidence bound at the 95% confidence level for the true proportion of such hips that develop squeaking. (b) Interpret the 95% confidence level used in (a). We are 95% confident that the true proportion of all such artificial hip recipients who experience squeaking is less than the lower bound. We are 95% confident that the true proportion of all such artificial hip recipients who experience squeaking is greater than the lower bound. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

Q4.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=247
Sample Size(n)=356
Sample proportion = x/n =0.694
Confidence Interval = [ 0.694 ±Z a/2 ( Sqrt ( 0.694*0.306) /356)]
= [ 0.694 - 1.96* Sqrt(0.001) , 0.694 + 1.96* Sqrt(0.001) ]
= [ 0.646,0.742]
Interpretations:
1) We are 95% sure that the interval [0.646 , 0.742 ] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion  

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