document.write( "Question 1199228: We sampled 800 NY teachers for their annual income. In our sample,
\n" ); document.write( "the average annual income is $60,000 and the standard deviation of annual
\n" ); document.write( "incomes is $7,500. Based on that sample, we want to predict the mean annual
\n" ); document.write( "income μ of all the NY teachers with the confidence level of 0.99 (99 percent).
\n" ); document.write( "Part a) What prediction do we make about μ?
\n" ); document.write( "Part b) What is the error bound/margin E in that prediction? \n" ); document.write( "
Algebra.Com's Answer #833009 by Theo(13342)\"\" \"About 
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sample size is 800
\n" ); document.write( "sample mean is 60,000.
\n" ); document.write( "sample standard deviation = 7500.
\n" ); document.write( "two tailed confidence interval is 99% = .99
\n" ); document.write( "alpha on each end of the confidence interval is .5% = .005
\n" ); document.write( "for 99% confidence interval, the critical t-score, at 799 degrees of confidence, is plus or minus 2.581997 rounded to 6 decimal places.
\n" ); document.write( "the standard error of the distribution of sample means is equal to the standard deviation of the sample divided by the square root of the sample size.
\n" ); document.write( "the standard error is therefore 7500/sqrt(800) = 265.165 rounded to 3 decimal places.
\n" ); document.write( "use the critical t-score to find the critical sample mean score.
\n" ); document.write( "the formula is t = (x - m) / s
\n" ); document.write( "t is the t-score
\n" ); document.write( "x is the sample mean
\n" ); document.write( "m is the assumed population mean
\n" ); document.write( "s is the standard error.
\n" ); document.write( "you are looking for the margin of error.
\n" ); document.write( "that would be represented by (x - m)
\n" ); document.write( "on the low side, the t-score formula becomes:
\n" ); document.write( "-2.581997 = (60,000 - m) / 265.165
\n" ); document.write( "solve for 60,000 - m to get (60,000 - m) = -684.655 rounded to 3 decimal places.
\n" ); document.write( "on the high side, the t-score formula becomes:
\n" ); document.write( "2.581997 = (60,000 - m) / 265.165
\n" ); document.write( "solve for 60,000 - m to get (60,000 - m) = 684.655
\n" ); document.write( "your margin of error is 684.655 on both sides of the assumed population mean.
\n" ); document.write( "that would make the estimate of the population mean between (60,000 - 685) and (60,000 + 685) = 59315 and 60685.
\n" ); document.write( "i don't have a t-score graphing calculator that will show the raw score analysis on a graph, but i do have a z-score calculator that will do that, after manipulation of the confidence interval to make the t-score look like the z-score.
\n" ); document.write( "this is what it looks like.
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