document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179648>Question 179648</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" );
document.write( "3.087 3.131 3.241 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. (b) What sample size<BR>\n" );
document.write( "would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?<BR>\n" );
document.write( "(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during<BR>\n" );
document.write( "manufacture. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134652 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=134652\">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<BR>\n" );
document.write( "3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477<BR>\n" );
document.write( "x-bar = 3.305 ; s =0.132.. ; n= 10<BR>\n" );
document.write( "-----------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "(a) Construct a 90 percent confidence interval for the true mean weight.<BR>\n" );
document.write( "E = 1.645[0.132/sqrt(10)] = 0.069.. <BR>\n" );
document.write( "---<BR>\n" );
document.write( "90% CI: 3.305-0.069 < u < 3.305+0.069<BR>\n" );
document.write( "------------------------------------<BR>\n" );
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( "n = [z*s/E]^2 = [1.645*0.132/0.03]^2 = 52.39; rounding up n = 53\r<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.<BR>\n" );
document.write( "humidity level; machine variability; manufacture tolerance<BR>\n" );
document.write( "==============================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );