Question 1129146
A.  sample proportion(P) = 322/2023 = 0.1592
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Standard Error(SE) of P = square root(0.1592 * (1-0.1592) / 2023) = 0.0001
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Margin of error(ME) = Critical value(CV) x SE of P
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Since the sample size is sufficiently large, that is, sample size is greater than 30, we can use the Normal Distribution to determine CV
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To determine the CV for a confidence level use the following steps
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alpha = 1 - (confidence level/100)
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critical probability(p*) = 1 - (a/2)
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CV is the z-score associated with p*
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CV for a 90% confidence level is 1.645
CV for a 95% confidence level is 1.960
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C.
ME for 90% = 1.645 * 0.0001 = 0.0001645 is approximately 0.0002
ME for 95% = 1.960 * 0.0001 = 0.0001960 is approximately 0.0002
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D. 0.1592 + or - 0.0002 is (0.1590, 0.1594)
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E. 0.1592 + or - 0.0002 is (0.1590, 0.1594)
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Note the problem does not state the accuracy level so rounding to 4 significant digits yields the same confidence interval for D and E
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