document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922878>Question 922878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dylan Jones kept careful records of the fuel efficiency of his new car. After the first thirteen times he filled up the tank, he found the mean was 25.6 miles per gallon (mpg) with a sample standard deviation of .9 mpg.<BR>\n" );
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document.write( "Compute the 95 percent confidence interval for his mpg. (Round your answers to 3 decimal places.)<BR>\n" );
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document.write( "  The confidence interval is between ... and .... \r<BR>\n" );
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document.write( "(b) <BR>\n" );
document.write( "How many times should he fill his gas tank to obtain a margin of error below 0.2 mpg? (Round your answer to the nearest whole number.)<BR>\n" );
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document.write( "  Number of times    \r<BR>\n" );
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document.write( "If you don't mind, please show your work. I will greatly appreciate it! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559756 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=559756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Dylan Jones kept careful records of the fuel efficiency of his new car. After the first thirteen times he filled up the tank, he found the mean was 25.6 miles per gallon (mpg) with a sample standard deviation of .9 mpg.<BR>\n" );
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document.write( "Compute the 95 percent confidence interval for his mpg. (Round your answers to 3 decimal places.)<BR>\n" );
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document.write( "CI:: x-bar - z(s/sqrt(n)) < u < x-bar + z(s/sqrt(n)<BR>\n" );
document.write( "x-bar = 25.6<BR>\n" );
document.write( "ME = z*s/sqrt(n)<BR>\n" );
document.write( "ME = 1.96*0.9 = 1.276<BR>\n" );
document.write( "Note:: s/sqrt(n) is the standard deviation of the sample means<BR>\n" );
document.write( "You are told that the sample standard deviation is 0.9<BR>\n" );
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document.write( "Also, z is the z-value associated with a 2-tail test when alpha = 0.95<BR>\n" );
document.write( "That value is invNorm(0.975) = 1.96<BR>\n" );
document.write( "If you use a z-chart, find the z-value with 0.475 to the right of the mean. <BR>\n" );
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document.write( "95%CI:: 25.6-1.76 < u < 25.6+1.76<BR>\n" );
document.write( "95%CI:: 23.84 < u < 27.36<BR>\n" );
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document.write( "b) <BR>\n" );
document.write( "How many times should he fill his gas tank to obtain a margin of error below 0.2 mpg? (Round your answer to the nearest whole number.)<BR>\n" );
document.write( "s/sqrt(15) = 0.9<BR>\n" );
document.write( "s = 3.486<BR>\n" );
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document.write( "ME = z*s/sqrt(n)<BR>\n" );
document.write( "Solve 1.96*3.486/sqrt(n) < 0.2<BR>\n" );
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document.write( "sqrt(n) > 1.96*3.486/0.2<BR>\n" );
document.write( "sqrt(n) > 34.16<BR>\n" );
document.write( "n > 1167 times<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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