document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136270>Question 136270</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 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477\r<BR>\n" );
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document.write( "construct a 90 percent confidence interval for the true mean weight. <BR>\n" );
document.write( "what sample size would be necessary to estimate the true weight with an error of + 0.03 grams with 90 percent confidence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99818 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=99818\">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<BR>\n" );
document.write( "a very accurate scale. The results in grams were<BR>\n" );
document.write( "3.087 3.131 3.3.241 3.270 3.353 3.400 3.411 3.437 3.477<BR>\n" );
document.write( "(a) Construct a 90 percent confidence interval for the true mean weight.<BR>\n" );
document.write( "E = z*sigma/sqrt(n)<BR>\n" );
document.write( "E = 1.645*0.13199/sqrt(10)<BR>\n" );
document.write( "E = 0.06866<BR>\n" );
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document.write( "x-bar = 3.3048<BR>\n" );
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document.write( "90% CI = (3.3048-0.06866 , 3.3048+0.06866)<BR>\n" );
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document.write( "(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?<BR>\n" );
document.write( "E = z*sigma/sqrt(n)<BR>\n" );
document.write( "n = [z*sigma/E]^2<BR>\n" );
document.write( "z* for 90% confidence = 1.645<BR>\n" );
document.write( "sigma = 0.13199<BR>\n" );
document.write( "E = 0.03<BR>\n" );
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document.write( "n = [1.645*0.13199/0.03]^2 = 52.38<BR>\n" );
document.write( "rounded up: n = 53<BR>\n" );
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document.write( "(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.<BR>\n" );
document.write( "Temperature; consistency of batches; machine tolerances<BR>\n" );
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document.write( "cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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