Vol. 12, No. 3
March 2010
PQ Systems
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Quality Quiz from Professor Cleary

Last month we met Quinn Quip, quality manager for Quince’s Quality Quiche in Quincy. In a market survey, Quinn wanted to determine the percent of outlets—restaurants, hotels, bakeries, and cafes, as well as private residents—in Quincy who sell or consume the quiche that his company makes. He took many samples of a (sample) size of 100. He found that on average 50 out of the 100 sampled use Quince’s Quality Quiche, and reported to his boss that half the town—give or take 2 percent—are customers.

While this assessment seems inconsistent with the sales reports that the company has generated, Quinn stood by his analysis. To verify the accuracy of this analysis last month, we referred to the binomial central limit theorem, which states that taking many samples of the size n in a population with a mean () of .50 and creating a histogram of the sample proportions would generate three facts about the distribution of sample proportions:

  • The mean would be close to , or .50 in this case;
  • The shape of the distribution would be non-normal;
  • The variability of the distribution would be equal to

or in Quinn’s case,

Consider the correctness of this analysis, and indicate whether the assertion is:

a) True

b) False

 

Click here for a more complete video explanation

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