document.write( "Question 1201598: n = 96, x = 79.7, 􏰀 = 6.0; 99% confidence \n" ); document.write( "
Algebra.Com's Answer #836184 by Theo(13342)\"\" \"About 
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not sure what you are looking for, but i would guess you are looking for the 99% confidence interval, using either the t-score or the z-score.
\n" ); document.write( "what i get is:
\n" ); document.write( "sample size is 96.
\n" ); document.write( "either sample mean 79.7.
\n" ); document.write( "either sample standard deviation or population standard deviation is 6.
\n" ); document.write( "if you are dealing with the population standard deviation, then use of the z-score is implied.
\n" ); document.write( "if you are dealing with the sample standard deviation, then use of the t-score would be implied.
\n" ); document.write( "because the sample size is large, there shouldn't be a large difference between them.
\n" ); document.write( "since you are looking for the mean of a sample of specified size, the standard error is used rather than the standard deviation.
\n" ); document.write( "standard error = standard deviation / square root of sample size = 6 / sqrt(96) = .6123724357.\r
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\n" ); document.write( "\n" ); document.write( "99% confidence interval using the z-score gets you critical z = plus or minus 2.575829303.
\n" ); document.write( "use the z-score formula to get the raw score.
\n" ); document.write( "on the high side, z = (x - m) / s becomes 2.575829303 = (x - 79.7) / .6123724357.
\n" ); document.write( "solve for x to get x = 2.575829303 * .6123724357 + 79.7 = 81.27736686.
\n" ); document.write( "on the low side, z = (x - m) / s becomes -2.575829303 = (x - 79.7) / .6123724357.
\n" ); document.write( "solve for x to get x = -2.575829303 * .6123724357 + 79.7 = 78.12263314.
\n" ); document.write( "your 99% confidence interval using the z-score is from 78.12263314 to 81.27736686. *****\r
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\n" ); document.write( "\n" ); document.write( "99% confidence interval using the t-score gets you critical t with 95 degrees of freedom = plus or minus 2.628575664.
\n" ); document.write( "use the t-score formula to get the raw score.
\n" ); document.write( "on the high side, t = (x - m) / s becomes 2.628575664 = (x - 79.7) / .6123724357.
\n" ); document.write( "solve for x to get x = 2.628575664 * .6123724357 + 79.7 = 81.30966728.
\n" ); document.write( "on the low side, t = (x - m) / s becomes -2.628575664 = (x - 79.7) / .6123724357.
\n" ); document.write( "solve for x to get x = -2.628575664 * .6123724357 + 79.7 = 78.09033272.
\n" ); document.write( "your 99% confidence interval using the t-score is from 78.09033272 to 81.30966728. *****\r
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\n" ); document.write( "\n" ); document.write( "as you can see, the differnce becween z-score confidence interval and t-score confidence interval is not large.
\n" ); document.write( "this is because the sample size is large.
\n" ); document.write( "if the sample size was smaller (less than 20 or so), the difference would be more pronounced.
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