document.write( "Question 59559: Here is the problem and I honestly am not sure what to do. Is Sample size all voters in U.S or there is a computation to be done? \r
\n" ); document.write( "\n" ); document.write( " A New York Times article about Poll results states, \"In theory, in 19 cases out of 20, the results from such a poll should differ by no more than one percentage point in either direction from what would have been obtained by interviewing all voters in the United States. Find the sample size suggested by this statement. \n" ); document.write( "
Algebra.Com's Answer #40829 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Here is the problem and I honestly am not sure  what to do. Is Sample size all\r\n" );
document.write( "voters in U.S or there is a computation to be done? \r\n" );
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document.write( "A New York Times article about Poll results states, \"In theory, in 19 cases out\r\n" );
document.write( "of 20, the results from such a poll should differ by no more than one\r\n" );
document.write( "percentage point in either direction from what would have been obtained by\r\n" );
document.write( "interviewing all voters in the United States. Find the sample size suggested by\r\n" );
document.write( "this statement.\r\n" );
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document.write( "We do not need the standard deviation s as the previous \r\n" );
document.write( "tutor stated. We do not even need an estimate of the\r\n" );
document.write( "proportion who will say \"yes\".  The previous tutor \r\n" );
document.write( "also gave the wrong value for z.  He gave\r\n" );
document.write( "za/2 = z0.01/2 = z0.005 = 2.5758.  That's wrong. He should \r\n" );
document.write( "have given\r\n" );
document.write( "za/2 = z0.05/2 = z0.025 = 1.96\r\n" );
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document.write( "We use the formula. He also gave the wrong formula. \r\n" );
document.write( "This is a proportion problem.\r\n" );
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document.write( "       ^^\r\n" );
document.write( "     z2pq\r\n" );
document.write( "n = -----\r\n" );
document.write( "      E2\r\n" );
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document.write( "We will assume this is a poll where people\r\n" );
document.write( "polled answer \"yes, I will vote for the candidate\"\r\n" );
document.write( "or \"no, I will not vote for the candidate\".\r\n" );
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document.write( "The confidence level is 19 out of 20, that is,\r\n" );
document.write( "19/20, which equals 0.95.  From the standard\r\n" );
document.write( "normal tables, we know that  \r\n" );
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document.write( "P(-1.96 < z < 1.96) = 0.95\r\n" );
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document.write( "so we use z = 1.96\r\n" );
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document.write( "(this is often written za/2 = z0.05/2 = z0.025 = 1.96)\r\n" );
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document.write( "Now E represents the maximum allowable error,\r\n" );
document.write( "which, the words \"no more than one percentage point\r\n" );
document.write( "in either direction\" tells us that E = 1% = 0.01\r\n" );
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document.write( "                   ^    ^\r\n" );
document.write( "Now we do not know p or q, the estimated proportions\r\n" );
document.write( "of people who will say \"yes\" and \"no\" respectively.\r\n" );
document.write( "However since they will be multiplied together in\r\n" );
document.write( "the formula, the most their product can possibly be\r\n" );
document.write( "is when they are both 0.5. Why this is true can be \r\n" );
document.write( "shown from this table:\r\n" );
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document.write( "   ^           ^          ^^\r\n" );
document.write( "If p is   then q is   and pq =\r\n" );
document.write( "   0.0      1.0          0.0  \r\n" );
document.write( "   0.1      0.9          0.09\r\n" );
document.write( "   0.2      0.8          0.16\r\n" );
document.write( "   0.3      0.7          0.21\r\n" );
document.write( "   0.4      0.6          0.24\r\n" );
document.write( "   0.5      0.5          0.25 <--(largest value in list)\r\n" );
document.write( "   0.6      0.4          0.24\r\n" );
document.write( "   0.7      0.3          0.21\r\n" );
document.write( "   0.8      0.2          0.16\r\n" );
document.write( "   0.9      0.1          0.09\r\n" );
document.write( "   1.0      0.0          0.00 \r\n" );
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document.write( "          ^           ^ \r\n" );
document.write( "so we use p = 0.5 and q = 0.5,\r\n" );
document.write( "and    \r\n" );
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document.write( "       ^^\r\n" );
document.write( "     z2pq\r\n" );
document.write( "n = ------\r\n" );
document.write( "       E2\r\n" );
document.write( "\r\n" );
document.write( "becomes\r\n" );
document.write( "     (1.96)2(0.5)(0.5) \r\n" );
document.write( "n = ------------------\r\n" );
document.write( "         (0.01)2\r\n" );
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document.write( "n = 9604\r\n" );
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document.write( "So from the information given, we'd need to\r\n" );
document.write( "interview 9604 people at random to ensure\r\n" );
document.write( "that we can get the proportion within 1\r\n" );
document.write( "percentage point with a probability of 95%\r\n" );
document.write( "of being right.\r\n" );
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document.write( "Edwin
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