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Cigarette taxes New York public health officials report that currently 22% of adults smoke
They hope that newly increased state cigarette taxes will reduce this rate. They plan to check in December by selecting a random sample of 1200 New Yorkers to estimate again the percentage of adults who smoke.

a. Verify that a Normal model is a useful approximation for the binomial in this situation.
b. In that December sample, how many smokers would it take to convince you that the percentage of NY adults who smoke had decreased significantly? Explain.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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a. Conditions/Assumptions for Normal model must be satisfied.
np ≥ 10   (1200)(0.22) = 264 ≥ 10 and nq ≥ 10   (1200)(0.78) = 936 ≥ 10
1200 < 10% of all New Yorkers
b. It would be unusual to see the number of adult smokers be less than 2 or 3 standard deviations below the mean.  Since the standard deviation = = = 14.35, it would be unusual to see fewer than 235 (264 - 2(14.35) = 235.3) smokers. So, I would conclude that the estimate of 22% of adults smoke had decreased significantly if there were fewer than 235 smokers in the December sample of 1200 NY adults.
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