document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186540>Question 1186540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #8.3.9 (\"SOCR data 2008,\" 2013).  Compute a 95% confidence interval for the mean economic dynamism of middle-income countries.\r<BR>\n" );
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document.write( "Table #8.3.9: Economic Dynamism ($) of Middle Income Countries<BR>\n" );
document.write( "25.8057	37.4511	51.915	43.6952	47.8506	43.7178	58.0767<BR>\n" );
document.write( "41.1648	38.0793	37.7251	39.6553	42.0265	48.6159	43.8555<BR>\n" );
document.write( "49.1361	61.9281	41.9543	44.9346	46.0521	48.3652	43.6252<BR>\n" );
document.write( "50.9866	59.1724	39.6282	33.6074	21.6643		\r<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 #849428 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate a 95% confidence interval for the mean economic dynamism of middle-income countries based on the provided data:\r<BR>\n" );
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document.write( "**1. Calculate the Sample Mean (x̄):**\r<BR>\n" );
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document.write( "Sum all the economic dynamism values and divide by the number of values (n = 25).\r<BR>\n" );
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document.write( "x̄ = (25.8057 + 37.4511 + ... + 21.6643) / 25<BR>\n" );
document.write( "x̄ ≈ 43.8727\r<BR>\n" );
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document.write( "**2. Calculate the Sample Standard Deviation (s):**\r<BR>\n" );
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document.write( "This measures the spread of the data.  You can use a calculator or statistical software to find this.\r<BR>\n" );
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document.write( "s ≈ 9.5626\r<BR>\n" );
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document.write( "**3. Find the Critical t-value:**\r<BR>\n" );
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document.write( "Since the sample size is small (n < 30), we use the t-distribution.  For a 95% confidence level and 24 degrees of freedom (n - 1 = 25 - 1 = 24), the critical t-value is approximately 2.064. You can find this using a t-table or a statistical calculator.\r<BR>\n" );
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document.write( "**4. Calculate the Margin of Error (ME):**\r<BR>\n" );
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document.write( "ME = t * (s / √n)<BR>\n" );
document.write( "ME = 2.064 * (9.5626 / √25)<BR>\n" );
document.write( "ME ≈ 3.9934\r<BR>\n" );
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document.write( "**5. Calculate the Confidence Interval:**\r<BR>\n" );
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document.write( "*   Lower Bound = x̄ - ME = 43.8727 - 3.9934 ≈ 39.8793<BR>\n" );
document.write( "*   Upper Bound = x̄ + ME = 43.8727 + 3.9934 ≈ 47.8661\r<BR>\n" );
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document.write( "**Result:**\r<BR>\n" );
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document.write( "The 95% confidence interval for the mean economic dynamism of middle-income countries is approximately (39.8793, 47.8661).\r<BR>\n" );
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document.write( "**Interpretation:**\r<BR>\n" );
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document.write( "We are 95% confident that the true mean economic dynamism for all middle-income countries lies within this interval. This means that if we were to repeat this study many times, 95% of the calculated confidence intervals would contain the true population mean.<BR>\n" );
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