document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193654>Question 193654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were<BR>\n" );
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document.write( "3.28 <BR>\n" );
document.write( "3.25 <BR>\n" );
document.write( "3.25 <BR>\n" );
document.write( "3.3 <BR>\n" );
document.write( "3.33 <BR>\n" );
document.write( "3.36 <BR>\n" );
document.write( "3.07 <BR>\n" );
document.write( "3.29 <BR>\n" );
document.write( "3.47 <BR>\n" );
document.write( "3.4 \r<BR>\n" );
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document.write( "(a)Construct a 95 percent confidence interval for the true mean weight.<BR>\n" );
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document.write( "(b) What sample size would be necessary to estimate the true weight with an error of ± 0.02 grams with 95 percent confidence?<BR>\n" );
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document.write( "(c) What factors might cause variation in the weight of Tootsie Rolls during manufacture?<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 #145446 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=145446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were\r<BR>\n" );
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document.write( "3.28 <BR>\n" );
document.write( "3.25 <BR>\n" );
document.write( "3.25 <BR>\n" );
document.write( "3.3 <BR>\n" );
document.write( "3.33 <BR>\n" );
document.write( "3.36 <BR>\n" );
document.write( "3.07 <BR>\n" );
document.write( "3.29 <BR>\n" );
document.write( "3.47 <BR>\n" );
document.write( "3.4 \r<BR>\n" );
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document.write( "(a)Construct a 95 percent confidence interval for the true mean weight.<BR>\n" );
document.write( "x-bar: add them up and divide by 10 to get 3.3 and s = 0.1064<BR>\n" );
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document.write( "E ?: Using df=9 you get t= 2.262<BR>\n" );
document.write( "E = 2.262*s/sqrt(n) = 2.262*0.1064/sqrt(10) = 0.07611<BR>\n" );
document.write( "95% C.I.: 3.3-0.07611 < u < 3.3+0.0.07611<BR>\n" );
document.write( "95% C.I.: 3.2239 < u < 3.3761<BR>\n" );
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document.write( "(b) What sample size would be necessary to estimate the true weight with an error of ± 0.02 grams with 95 percent confidence?<BR>\n" );
document.write( "sqrt(n) = z*0.1064/E<BR>\n" );
document.write( "sqrt(n) = 1.96*0.064/0.02<BR>\n" );
document.write( "n = 39.338<BR>\n" );
document.write( "Rounding up: n = 40<BR>\n" );
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document.write( "(c) What factors might cause variation in the weight of Tootsie Rolls during manufacture?<BR>\n" );
document.write( "I'll leave that up to your imagination.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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