document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208176>Question 1208176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the relationship between level of confidence and sample needed, given other parameters are constant? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846441 by </B><A HREF=/tutors/aboutme.mpl?userid=PPCHLOE><B>PPCHLOE(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PPCHLOE><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/cgi-bin/show-face.mpl?user=PPCHLOE><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the solution to your statistics problem.Hope you find this helpful.<BR>\n" );
document.write( "Let's break it down step by step:<BR>\n" );
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document.write( "*Given parameters:*\r<BR>\n" );
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document.write( "- Constant population size (N)<BR>\n" );
document.write( "- Constant margin of error (E)<BR>\n" );
document.write( "- Constant desired confidence level (Z-score)\r<BR>\n" );
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document.write( "*Question:* How does the level of confidence affect the sample size needed?\r<BR>\n" );
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document.write( "*Step 1: Understand the formula*\r<BR>\n" );
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document.write( "The sample size (n) formula is:\r<BR>\n" );
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document.write( "n = (Z^2 * σ^2) / E^2\r<BR>\n" );
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document.write( "where:<BR>\n" );
document.write( "- n = sample size<BR>\n" );
document.write( "- Z = Z-score (related to confidence level)<BR>\n" );
document.write( "- σ = population standard deviation<BR>\n" );
document.write( "- E = margin of error\r<BR>\n" );
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document.write( "*Step 2: Analyze the Z-score*\r<BR>\n" );
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document.write( "The Z-score increases as the confidence level increases. For example:<BR>\n" );
document.write( "- 80% confidence: Z ≈ 1.28<BR>\n" );
document.write( "- 90% confidence: Z ≈ 1.645<BR>\n" );
document.write( "- 95% confidence: Z ≈ 1.96<BR>\n" );
document.write( "- 99% confidence: Z ≈ 2.576\r<BR>\n" );
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document.write( "*Step 3: Observe the relationship*\r<BR>\n" );
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document.write( "As the confidence level increases (Z-score increases), the sample size (n) also increases.\r<BR>\n" );
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document.write( "*Step 4: Explain the relationship*\r<BR>\n" );
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document.write( "A higher confidence level requires a larger sample size to achieve the same margin of error. This is because a higher confidence level means we want to be more certain about our results, which requires more data.\r<BR>\n" );
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document.write( "*In summary:*\r<BR>\n" );
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document.write( "- As the level of confidence increases, the sample size needed also increases.<BR>\n" );
document.write( "- This is because a higher confidence level requires more data to achieve the same margin of error.<BR>\n" );
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document.write( "If you're satisfied with my solution and interested in further learning , I'm available for a one-on-one online session. I'd be happy to share my knowledge and provide guidance to you personally. ogunjimio79@gmail.com\r<BR>\n" );
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document.write( " </SPAN>\n" );
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