document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980413>Question 980413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the standard normal distribution or the&#8203; t-distribution to construct a <BR>\n" );
document.write( "98% confidence interval for the population mean. <BR>\n" );
document.write( "The gas mileages&#8203; (in miles per&#8203; gallon) of 45 randomly selected cars are listed below.\r<BR>\n" );
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document.write( "2121 \r<BR>\n" );
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document.write( "2424 \r<BR>\n" );
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document.write( "1616 \r<BR>\n" );
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document.write( "2727 \r<BR>\n" );
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document.write( "1313 \r<BR>\n" );
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document.write( "2323 \r<BR>\n" );
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document.write( "1818 \r<BR>\n" );
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document.write( "1919 \r<BR>\n" );
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document.write( "1919 \r<BR>\n" );
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document.write( "1515 \r<BR>\n" );
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document.write( "1616 \r<BR>\n" );
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document.write( "1414 \r<BR>\n" );
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document.write( "2424 \r<BR>\n" );
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document.write( "1717 \r<BR>\n" );
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document.write( "2727 \r<BR>\n" );
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document.write( "   \r<BR>\n" );
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document.write( "2222 \r<BR>\n" );
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document.write( "2222 \r<BR>\n" );
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document.write( "1818 \r<BR>\n" );
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document.write( "1414 \r<BR>\n" );
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document.write( "1515 \r<BR>\n" );
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document.write( "1313 \r<BR>\n" );
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document.write( "1919 \r<BR>\n" );
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document.write( "1818 \r<BR>\n" );
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document.write( "2727 \r<BR>\n" );
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document.write( "2222 \r<BR>\n" );
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document.write( "2222 \r<BR>\n" );
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document.write( "1515 \r<BR>\n" );
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document.write( "1515 \r<BR>\n" );
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document.write( "2626 \r<BR>\n" );
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document.write( "1414 \r<BR>\n" );
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document.write( "2020 \r<BR>\n" );
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document.write( "1919 \r<BR>\n" );
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document.write( "2525 \r<BR>\n" );
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document.write( "2626 \r<BR>\n" );
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document.write( "1414 \r<BR>\n" );
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document.write( "2222 \r<BR>\n" );
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document.write( "2626 \r<BR>\n" );
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document.write( "1818 \r<BR>\n" );
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document.write( "1616 \r<BR>\n" );
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document.write( "1919 \r<BR>\n" );
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document.write( "2121 \r<BR>\n" );
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document.write( "2727 \r<BR>\n" );
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document.write( "2424 \r<BR>\n" );
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document.write( "2424 \r<BR>\n" );
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document.write( "2020 <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601545 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=601545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mpg data values are in <font color=\"red\">red</font>. The other numbers in black are row numbers to keep track of all of the data in a neater form (compared to one long column of 45 values).\r<BR>\n" );
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document.write( "<tr><th></th><th colspan=\"3\">Mileage (mpg)</th></tr><tr><TD >1</TD><TD ><font color=\"red\">21</font></TD><TD ><font color=\"red\">22</font></TD><TD ><font color=\"red\">20</font></TD></tr><tr><TD >2</TD><TD ><font color=\"red\">24</font></TD><TD ><font color=\"red\">22</font></TD><TD ><font color=\"red\">19</font></TD></tr><tr><TD >3</TD><TD ><font color=\"red\">16</font></TD><TD ><font color=\"red\">18</font></TD><TD ><font color=\"red\">25</font></TD></tr><tr><TD >4</TD><TD ><font color=\"red\">27</font></TD><TD ><font color=\"red\">14</font></TD><TD ><font color=\"red\">26</font></TD></tr><tr><TD >5</TD><TD ><font color=\"red\">13</font></TD><TD ><font color=\"red\">15</font></TD><TD ><font color=\"red\">14</font></TD></tr><tr><TD >6</TD><TD ><font color=\"red\">23</font></TD><TD ><font color=\"red\">13</font></TD><TD ><font color=\"red\">22</font></TD></tr><tr><TD >7</TD><TD ><font color=\"red\">18</font></TD><TD ><font color=\"red\">19</font></TD><TD ><font color=\"red\">26</font></TD></tr><tr><TD >8</TD><TD ><font color=\"red\">19</font></TD><TD ><font color=\"red\">18</font></TD><TD ><font color=\"red\">18</font></TD></tr><tr><TD >9</TD><TD ><font color=\"red\">19</font></TD><TD ><font color=\"red\">27</font></TD><TD ><font color=\"red\">16</font></TD></tr><tr><TD >10</TD><TD ><font color=\"red\">15</font></TD><TD ><font color=\"red\">22</font></TD><TD ><font color=\"red\">19</font></TD></tr><tr><TD >11</TD><TD ><font color=\"red\">16</font></TD><TD ><font color=\"red\">22</font></TD><TD ><font color=\"red\">21</font></TD></tr><tr><TD >12</TD><TD ><font color=\"red\">14</font></TD><TD ><font color=\"red\">15</font></TD><TD ><font color=\"red\">27</font></TD></tr><tr><TD >13</TD><TD ><font color=\"red\">24</font></TD><TD ><font color=\"red\">15</font></TD><TD ><font color=\"red\">24</font></TD></tr><tr><TD >14</TD><TD ><font color=\"red\">17</font></TD><TD ><font color=\"red\">26</font></TD><TD ><font color=\"red\">24</font></TD></tr><tr><TD >15</TD><TD ><font color=\"red\">27</font></TD><TD ><font color=\"red\">14</font></TD><TD ><font color=\"red\">20</font></TD></tr>\n" );
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document.write( "n = 45 is the sample size. Since n > 30, we can use a standard normal distribution instead of the T distribution.\r<BR>\n" );
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document.write( "Use a calculator to find\r<BR>\n" );
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document.write( "sample mean: xbar = 19.911111<BR>\n" );
document.write( "sample standard deviation: s = 4.378783<BR>\n" );
document.write( "critical value: z = 2.326 (at 98% confidence)\r<BR>\n" );
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document.write( "Optionally, you can use a table like <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">this one</a> to find the critical z value. Look in the bottom \"Z\" row and above the \"98%\" confidence level to find z = 2.326\r<BR>\n" );
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document.write( "The confidence interval is of the form (L,U) where L is the lower limit and U is the upper limit.\r<BR>\n" );
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document.write( "Lower Limit (L):<BR>\n" );
document.write( "L = xbar - z*s/sqrt(n)<BR>\n" );
document.write( "L = 19.911111 - 2.326*4.378783/sqrt(45)<BR>\n" );
document.write( "L = 19.911111 - 2.326*0.652750429781364<BR>\n" );
document.write( "L = 19.911111 - 1.51829749967145<BR>\n" );
document.write( "L = 18.3928135003285<BR>\n" );
document.write( "L = 18.39\r<BR>\n" );
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document.write( "Upper Limit (U):<BR>\n" );
document.write( "U = xbar + z*s/sqrt(n)<BR>\n" );
document.write( "U = 19.911111 + 2.326*4.378783/sqrt(45)<BR>\n" );
document.write( "U = 19.911111 + 2.326*0.652750429781364<BR>\n" );
document.write( "U = 19.911111 + 1.51829749967145<BR>\n" );
document.write( "U = 21.4294084996715<BR>\n" );
document.write( "U = 21.43\r<BR>\n" );
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document.write( "The 98% confidence interval for mu is (L,U) = <font size=5 color=\"red\">(18.39, 21.43)</font> (rounded to 2 decimal places)\r<BR>\n" );
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document.write( "Side Note: the margin of error is approximately 1.51829749967145<BR>\n" );
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