document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185365>Question 185365</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh>Applied Statistics in Business & Economics</A><BR>\n" );
document.write( ": <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 (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of � 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139036 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=139036\">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" );
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document.write( "Find the sample mean: I'll call it \"m\"=3.30480 <BR>\n" );
document.write( "Find the standard deviation of the sample: I'll call it \"s\" = 0.13199.<BR>\n" );
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document.write( "(a) Construct a 90 percent confidence interval for the true mean weight.<BR>\n" );
document.write( "Find the \"standard error\" which is designated \"E\".<BR>\n" );
document.write( "E = t*(s/sqrt(n)) = 1.833(0.13199/sqrt(10)) = 0.0765<BR>\n" );
document.write( "Then 90% CI is : m-E < u < m+E<BR>\n" );
document.write( "3.2283 < u < 3.3813<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" );
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document.write( "Use the \"E\" formula; but solve it for \"n\"<BR>\n" );
document.write( "n= (s/E)^2<BR>\n" );
document.write( "n = {0.13199/0.03)^2 = 19.35<BR>\n" );
document.write( "Rounding up you get n = 20<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" );
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document.write( "I'll leave that to you.<BR>\n" );
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document.write( "Question: I amswered this question several weeks ago, so I went<BR>\n" );
document.write( "to the file of \"answered Probability and Statistics problems\"<BR>\n" );
document.write( "and copied my old answer.  Can you enlighten me as to why you<BR>\n" );
document.write( "did not find the answer to your question there?  The vast <BR>\n" );
document.write( "majority of word problems from the Doane and Seward Stat book<BR>\n" );
document.write( "can be found in that file.<BR>\n" );
document.write( "Just wondered.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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