document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193583>Question 1193583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You want to obtain a sample to estimate the average number of hours per week community college students in the United States work at their job while being a full-time student. Based on previous evidence, you believe the population standard deviation is 10. You would like to be 99% confident that your estimate is within 1.5 hours of the true population mean. <BR>\n" );
document.write( "Assume that the number of statistics students is unknown, but very large. How large of a sample size is required? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848643 by </B><A HREF=/tutors/aboutme.mpl?userid=yurtman><B>yurtman(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=yurtman><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Define the parameters:**\r<BR>\n" );
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document.write( "* **Confidence level:** 99%<BR>\n" );
document.write( "* **Margin of error (E):** 1.5 hours<BR>\n" );
document.write( "* **Population standard deviation (σ):** 10 hours\r<BR>\n" );
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document.write( "**2. Find the Z-score:**\r<BR>\n" );
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document.write( "* For a 99% confidence level, the Z-score is 2.576 (found using a standard normal distribution table or calculator).\r<BR>\n" );
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document.write( "**3. Calculate the required sample size (n):**\r<BR>\n" );
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document.write( "* Use the formula: <BR>\n" );
document.write( "   n = (Z-score * σ / E)² <BR>\n" );
document.write( "* Substitute the values: <BR>\n" );
document.write( "   n = (2.576 * 10 / 1.5)² <BR>\n" );
document.write( "* Calculate: <BR>\n" );
document.write( "   n ≈ 294.81\r<BR>\n" );
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document.write( "**4. Round up:**\r<BR>\n" );
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document.write( "* Since we can't have a fraction of a student, round up the sample size to the nearest whole number.\r<BR>\n" );
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document.write( "**Therefore, a sample size of 295 community college students is required to be 99% confident that the estimate of the average number of hours worked per week is within 1.5 hours of the true population mean.**<BR>\n" );
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