document.write( "Question 1210349: A random sample of 16 pharmacy customers showed the waiting times below (in minutes).\r
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Algebra.Com's Answer #852008 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I decided to do a recently posted statistics problem.  \r\n" );
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document.write( "Not because I like them, I don't. But because high schools and colleges are\r\n" );
document.write( "striving to make math courses practical in the workplace.  \r\n" );
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document.write( "Face it, algebra, geometry, and trig are no longer practical in any workplace,\r\n" );
document.write( "for computers do it all.  Engineers these days do nothing but point and click.\r\n" );
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document.write( "Statistics is the only thing that's still practical in nearly every field.\r\n" );
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document.write( "So schools began to push statistics, because it only requires first year\r\n" );
document.write( "algebra, and with computers doing all the substituting in formulas, even\r\n" );
document.write( "less.\r\n" );
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document.write( "When high schools began pushing statistics, this site at first had a\r\n" );
document.write( "deluge of statistics problems posted.  \r\n" );
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document.write( "However, no tutors on here would bother solving them, including yours truly, so\r\n" );
document.write( "students learned this site was no good for posting stats problems, and this site\r\n" );
document.write( "went to pot.  \r\n" );
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document.write( "So if you tutors want to see this site start thriving again, you'd better start\r\n" );
document.write( "solving statistics problems. For that's the only way to salvage it.  \r\n" );
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document.write( "Face it, finding such things as integer solutions to randomly made-up equations\r\n" );
document.write( "are as impractical in the workplace as making mud pies.\r\n" );
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document.write( "Anyway, here's my stab at a t-problem.  My stats knowledge is getting rusty.\r\n" );
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document.write( "Count these data.  There are 16.  This is less than (or equal to) 30. That's\r\n" );
document.write( "considered a small sample.  So we will use the t-distribution, not the \r\n" );
document.write( "normal z-distribution.\r\n" );
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document.write( "20 14 23 22 22 15 21 18\r\n" );
document.write( "23 17 14 25 15 21 20 14\r\n" );
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document.write( "Add them, get 304\r\n" );
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document.write( "Divide by 16, get \r\n" );
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document.write( "We want the standard deviation, s. \r\n" );
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document.write( "Get the deviations from the mean, by subtracting 19 from each of those in the\r\n" );
document.write( "list.\r\n" );
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document.write( " 1 -5  4  3  3 -4  2 -1\r\n" );
document.write( " 4 -2 -5  6 -4  2  1 -5\r\n" );
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document.write( "Square the deviations from the mean:\r\n" );
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document.write( " 1 25 16  9  9 16  4  1\r\n" );
document.write( "16  4 25 36 16  4  1 25\r\n" );
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document.write( "Add them, get 208 \r\n" );
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document.write( "Divide by n-1, or 16-1 or 15\r\n" );
document.write( "Get \r\n" );
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document.write( "Now the formula for the margin of error is \r\n" );
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document.write( "We calculate \r\n" );
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document.write( "Since this is a 2-tailed test, 90 percent confidence interval leaves 10 percent\r\n" );
document.write( "on both ends, or half that, 0.05 on each end, giving the confidence interval of\r\n" );
document.write( "90 percent in between these two critical values.  \r\n" );
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document.write( "So we look up the t-value for the number of 15 (1 less than the number in the\r\n" );
document.write( "sample of 16) degrees of freedom for a 2-tailed test and find the value 1.753.\r\n" );
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document.write( "(or you can find the t-value on your TI-84 calculator by \r\n" );
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document.write( "2nd VARS area:0.95, df:15 ENTER ENTER ENTER, \r\n" );
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document.write( "and read more decimal values as 1.753050323)\r\n" );
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document.write( "That's the margin of error.  \r\n" );
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document.write( "The confidence interval is \r\n" );
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document.write( "(19-1.63199507,19+1.6199507) = (17.36800493, 20.63199507).\r\n" );
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document.write( "If you use a table of t-values you won't get that many decimal places.\r\n" );
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document.write( "Edwin

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