document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179488>Question 1179488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of 10-foot surgery patients had a mean weight of 240 pounds. The sample<BR>\n" );
document.write( "standard deviation was found to be pounds. Assuming that the foot surgery<BR>\n" );
document.write( "patients’ weights are normally distributed. Construct a 95% confidence interval for a<BR>\n" );
document.write( "sample for the true mean weight of all foot surgery patients. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850228 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=850228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It seems like there's a typo in the problem statement, and the sample standard deviation is missing. I'll assume the sample standard deviation is **20 pounds** to illustrate the process. If you have the correct value, you can plug it in and follow the same steps.\r<BR>\n" );
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document.write( "**Here's how to construct the 95% confidence interval:**\r<BR>\n" );
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document.write( "**1. Identify the given information:**\r<BR>\n" );
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document.write( "* Sample size (n) = 10<BR>\n" );
document.write( "* Sample mean (x̄) = 240 pounds<BR>\n" );
document.write( "* Sample standard deviation (s) = 20 pounds (assumed)<BR>\n" );
document.write( "* Confidence level = 95%\r<BR>\n" );
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document.write( "**2. Determine the degrees of freedom (df):**\r<BR>\n" );
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document.write( "df = n - 1 = 10 - 1 = 9\r<BR>\n" );
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document.write( "**3. Find the t-value:**\r<BR>\n" );
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document.write( "For a 95% confidence interval and 9 degrees of freedom, we need the t-value that leaves 2.5% in each tail (α/2 = 0.05/2 = 0.025).\r<BR>\n" );
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document.write( "Using a t-table or calculator, the t-value for df = 9 and α/2 = 0.025 is approximately 2.262.\r<BR>\n" );
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document.write( "**4. Calculate the margin of error (E):**\r<BR>\n" );
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document.write( "E = t * (s / √n) = 2.262 * (20 / √10) ≈ 14.28 pounds\r<BR>\n" );
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document.write( "**5. Construct the confidence interval:**\r<BR>\n" );
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document.write( "Confidence interval = x̄ ± E = 240 ± 14.28\r<BR>\n" );
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document.write( "Lower bound = 240 - 14.28 = 225.72 pounds<BR>\n" );
document.write( "Upper bound = 240 + 14.28 = 254.28 pounds\r<BR>\n" );
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document.write( "**Therefore, the 95% confidence interval for the true mean weight of all foot surgery patients is approximately (225.72 pounds, 254.28 pounds).**\r<BR>\n" );
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document.write( "**If you provide the correct sample standard deviation, I can recalculate the confidence interval with the accurate value.** </SPAN>\n" );
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