document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205508>Question 1205508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you solve the question below, I'll be appreciated.\r<BR>\n" );
document.write( "\n" );
document.write( "A statistics practitioner took a random sample of 48 observations from a population whose standard deviation is 24 and computed the sample mean to be 98.\r<BR>\n" );
document.write( "\n" );
document.write( "Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.\r<BR>\n" );
document.write( "\n" );
document.write( "A. Estimate the population mean with 95% confidence.\r<BR>\n" );
document.write( "\n" );
document.write( "Confidence Interval = ?\r<BR>\n" );
document.write( "\n" );
document.write( "B. Estimate the population mean with 95% confidence, changing the population standard deviation to 49;\r<BR>\n" );
document.write( "\n" );
document.write( "Confidence Interval = ?\r<BR>\n" );
document.write( "\n" );
document.write( "C. Estimate the population mean with 95% confidence, changing the population standard deviation to 6;\r<BR>\n" );
document.write( "\n" );
document.write( "Confidence Interval = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842372 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A statistics practitioner took a random sample of 48 observations from a population whose standard deviation is 24 and computed the sample mean to be 98.<BR>\n" );
document.write( "Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the standard deviation is taken from the population, the z-score is used.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A. Estimate the population mean with 95% confidence.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "critical z-score for two tailed 95% confidence interval is z = plus or minus 1.96.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/010311.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score formula is z = (x-m)/s<BR>\n" );
document.write( "z is the critical z-score.<BR>\n" );
document.write( "x is the critical raw score<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard error when you're looking for the mean of a sample.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sample size is 48.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = standard deviation / sqrt(sample size) = 24 / sqrt(48) = 3.4641 rounded to 4 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the high side of the confidence interval, z = (x-m)/s becomes 1.96 = (x-98)/3.4641.<BR>\n" );
document.write( "solve for x to get x = 1.96 * 3.4641 + 98 = 104.79 rounded to 2 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the low side of the confidence interval, z = (x-m)/s becomes -1.96 = (x-98)/3.4641.<BR>\n" );
document.write( "solve for x to get x = -1.96 * 3.4641 + 98 = 91.21 rounded to 2 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your 95% confidence limit is equal to (91.21,104.79).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/010312.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B. Estimate the population mean with 95% confidence, changing the population standard deviation to 49;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "population standard deviation = 49\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = standard deviation / sqrt(sample size) = 49 / sqrt(48) = 7.0725 rounded to 4 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "critical z-score for two tailed 95% confidence interval is z = plus or minus 1.96.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the high side of the confidence interval, z-score formula becomes 1.96 = (x-98)/7.0725.<BR>\n" );
document.write( "solve for x to get x = 1.96 * 7.0725 + 98 = 111.86 rounded to 2 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the low side of the confidence interval, z-score formula becomes -1.96 = (x-98)/7.0725.<BR>\n" );
document.write( "solve for x to get x = -1.96 * 7.0725 + 98 = 84.14 rounded to 2 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your 95% confidence limit is equal to (84.14,111.86).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/010313.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "C. Estimate the population mean with 95% confidence, changing the population standard deviation to 6;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "critical z-score for two tailed 95% confidence interval is z = plus or minus 1.96.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = standard deviation / sqrt(ample size) = 6 / sqrt(48) = .8660 rounded to 4 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the high side of the confidence interval, z-score formula becomes 1.96 = (x-98)/.8660.<BR>\n" );
document.write( "solve for x to get x = 1.96 * .8660 + 98 = 99.70 rounded to 2 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the low side of the confidence interval, z-score formula becomes -1.96 = (x-98)/.8660.<BR>\n" );
document.write( "solve for x to get x = -1.96 * .8660 + 98 = 96.30 rounded to 2 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your 95% confidence interval is equal to (96.30,99.70).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/010314.jpg\"><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );