Question 865023: Please help,
In a survey of 1001 U.S. adults, 27% said they smoked a cigarette in the past week. The survey's margin of error is plus or minus 3%. Translate this information into a confidence interval for p. Approximate the value of the level of confidence c. (Note: For this problem, you must calculate the value of c. Do not round to the nearest common value found in tables.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a survey of 1001 U.S. adults, 27% said they smoked a cigarette in the past week. The survey's margin of error is plus or minus 3%. Translate this information into a confidence interval for p. Approximate the value of the level of confidence c. (Note: For this problem, you must calculate the value of c. Do not round to the nearest common value found in tables.)
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sample proportion = p-hat = 0.27
ME = 0.03
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CI:: 0.27-0.03 < p < 0.27+0.03
CI: 0.24 < p < 0.30
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Level of confidence correlates with the z-value
ME = z*sqrt[pq/n]
0.03 = z*sqrt[0.27*0.73/1001]
z = 0.03/0.014
z = 2.1379
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normalcdf(2.1379) = 0.16
2*0.16 ~ 3%
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c ~ 3%
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Cheers,
Stan H.
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