document.write( "Question 173497: A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:
\n" ); document.write( " 0
\n" ); document.write( " 260
\n" ); document.write( " 356
\n" ); document.write( " 403
\n" ); document.write( " 536
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\n" ); document.write( " 268
\n" ); document.write( " 369
\n" ); document.write( " 428
\n" ); document.write( " 536
\n" ); document.write( "
\n" ); document.write( "268
\n" ); document.write( " 396
\n" ); document.write( " 469
\n" ); document.write( " 536
\n" ); document.write( " 162
\n" ); document.write( " 338
\n" ); document.write( " 403
\n" ); document.write( " 536
\n" ); document.write( " 536
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\n" ); document.write( " (a) Construct a 95 percent confidence interval for the true mean.b) Why might normality be an issue here?(c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence? (d) If this is not a reasonable requirement, suggest one that is. \r
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Algebra.Com's Answer #128534 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "(a) Construct a 95 percent confidence interval for the true mean.
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document.write( "On your TI-83 or 84 calculator\r\n" );
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document.write( "Press STAT then ENTER\r\n" );
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document.write( "Put all 20 numbers in L1\r\n" );
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document.write( "Press STAT, press right arrow once to highlight CALC\r\n" );
document.write( "Press ENTER twice.\r\n" );
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document.write( "You'll see some statistics come up on the screen\r\n" );
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document.write( "Press STAT then the right arrow twice to highlight TESTS\r\n" );
document.write( "Then press 8 to get T-Interval\r\n" );
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document.write( "You see the TInterval menu.\r\n" );
document.write( "Make sure Stats is highlighted\r\n" );
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document.write( "You should see:\r\n" );
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document.write( "TInterval\r\n" );
document.write( " Inpt:Data Stats\r\n" );
document.write( " x:346.5\r\n" );
document.write( " Sx:170.3783714...\r\n" );
document.write( " n:20\r\n" );
document.write( " C-Level:.95\r\n" );
document.write( " Calculate\r\n" );
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document.write( "Type .95 after C-Level if it's not there\r\n" );
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document.write( "Scroll down to highlight \"Calculate\"\r\n" );
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document.write( "Press ENTER\r\n" );
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document.write( "You should see \r\n" );
document.write( "TInterval\r\n" );
document.write( "(266.76,426.24)\r\n" );
document.write( "x=346.5\r\n" );
document.write( "Sx=170.3783715\r\n" );
document.write( "n=20\r\n" );
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document.write( "That's your confidence interval\r\n" );
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document.write( "(266.76,426.24)\r\n" );
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document.write( "or maybe your book writes it as \r\n" );
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document.write( "\"266.76+%3C+x+%3C+426.24\"\r\n" );
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document.write( "

\n" ); document.write( ".b) Why might normality be an issue here?
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document.write( "Because it is a small sample and we must assume\r\n" );
document.write( "that the data be nomally distributed.\r\n" );
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document.write( "

\n" ); document.write( "(c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence?
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document.write( "We use the formula:\r\n" );
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document.write( "First we find \"matrix%282%2C1%2Cz%5Balpha%2F2%5D%2C%22%22%29\"\r\n" );
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document.write( "Subtract .99 from 1, getting .01, then divide this by 2\r\n" );
document.write( "to get .005 \r\n" );
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document.write( "Press 2nd then VARS to get the DISTR menu\r\n" );
document.write( "Press 3 to get invNorm( on the main screen\r\n" );
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document.write( "then after InvNorm(, type .005 and close the\r\n" );
document.write( "parentheses, so that you see\r\n" );
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document.write( "InvNorm(.005)\r\n" );
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document.write( "on the main screen.\r\n" );
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document.write( "Press ENTER and you read -2.575829303\r\n" );
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document.write( "Now substitute in the formula:\r\n" );
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document.write( "Get 1926.030165\r\n" );
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document.write( "Round UP to 1927, (even though you were told in \r\n" );
document.write( "elementary school to round down when the first\r\n" );
document.write( "digit dropped is less than 5) \r\n" );
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document.write( "

\n" ); document.write( "(d) If this is not a reasonable requirement,
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\r\n" );
document.write( "This is not reasonable because there are only 1591 pages\r\n" );
document.write( "in the directory.\r\n" );
document.write( "

\n" ); document.write( "suggest one that is.
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\r\n" );
document.write( "Reduce the confidence level requirement to 90%.\r\n" );
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document.write( "Do the above using .9 instead of .99 and get\r\n" );
document.write( "that the sample size needed is 786, which is not\r\n" );
document.write( "unreasonable.\r\n" );
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document.write( "Edwin
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