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An investigator wishes to estimate the difference between population mean SAT-M scores of incoming freshmen in the College of Engineering and in the College of Science at Purdue University. The population standard deviations are both roughly 100 points and equal sample sizes are to be selected. What value of the common sample size $\mathrm{n}$ will be necessary to estimate the difference to within 10 points with $99 \%$ confidence?
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