document.write( "Question 1203901: You measure 45 backpacks' weights, and find they have a mean weight of 49 ounces. Assume the population standard deviation is 14.8 ounces. Based on this, what is the maximal margin of error associated with a 95% confidence interval for the true population mean backpack weight.\r
\n" ); document.write( "\n" ); document.write( "Give your answer as a decimal, to two places\r
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\n" ); document.write( " ounces \n" ); document.write( "
Algebra.Com's Answer #839804 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
i believe this is how you would solve this.\r
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\n" ); document.write( "\n" ); document.write( "population mean is 49
\n" ); document.write( "population standard deviation is 14.5
\n" ); document.write( "sample size is 45.\r
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\n" ); document.write( "\n" ); document.write( "standard error is equal to standard devition divided by square root of sample size = 14.5/sqrt(45) = 2.16153.\r
\n" ); document.write( "\n" ); document.write( "z-score formula is z = (x-m)/s
\n" ); document.write( "z is the z-score
\n" ); document.write( "x is the samp[le mean
\n" ); document.write( "m is the population mean
\n" ); document.write( "s is the standard error.\r
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\n" ); document.write( "\n" ); document.write( "95% confidence interval requires a z-score equal to plus or minus 1.95996.
\n" ); document.write( "that's a two tailed confience interval with 2.5% alpha on each end.
\n" ); document.write( "alpha is the area under the normal distribution curve that's not in the confidence interval.\r
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\n" ); document.write( "\n" ); document.write( "using the z-score formula, you get:
\n" ); document.write( "on the high side z = (x-m/s becoms 1.95996 = (x-49)/2.16153.
\n" ); document.write( "solve for (x-49) to get (x-49) = 1.95996 * 2.16153 = 4.23651.
\n" ); document.write( "that's your margin of error.
\n" ); document.write( "solve for x to get high side raw score = 53.236517.\r
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\n" ); document.write( "\n" ); document.write( "on the low side z = (x-m)/s becomes -1.95996 = (x-49)/2.16153.
\n" ); document.write( "solve for (x-49) to get (x-49) = -1.95996 * 2.16153 = -4.23651.
\n" ); document.write( "solve for x to get low side raw score = 44.76349.\r
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\n" ); document.write( "\n" ); document.write( "round ansswers to two decimql places to get:
\n" ); document.write( "margin of error = 4.24
\n" ); document.write( "minimum value = 44.76.
\n" ); document.write( "maximum value = 53.34.\r
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\n" ); document.write( "\n" ); document.write( "i used the calculator at https://davidmlane.com/hyperstat/z_table.html to confirm this answer is correct.
\n" ); document.write( "it is correct as long as you calculated the standard error correctly, which i think i did, and as long as my assumptions about what the problem is looking for is correct.\r
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\n" ); document.write( "\n" ); document.write( "here's what the results from the calculator look like.\r
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