Quality Quiz from Professor Cleary
Congratulations:
"B" is correct.
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This sample is known as a point estimate, assuming that the sample has been taken properly and was truly random. The next step is to create a sample proportion and build a confidence interval around it, just as we did with the we recently accounted. You may remember that a confidence interval for would be derived as follows:
(based on the central limit theorem)
This formula is for interval data, but of course this problem deals with proportional (ratio) data, so the formula that applies to this case is as follows:
(rounded)
or
What this translates to in language is, “My best estimate for the proportion of defects of Wipe Out caps is 10%. I can further state that I am 99% certain that the true proportion of defects is between 2% and 18%.”
A second method to present this information to others is what I call the CNN method. The alternative method:
For our case:
Occasionally, one might hear a report of a survey that indicates that, say, 10% of Americans prefer pencils to ballpoint pens, with the disclaimer for “a margin of error of 8%.” What this really means is that the confidence interval built around the point estimate of 10% is plus or minus 8%.
Both ways of expressing the concept are correct.
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