document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=506904>Question 506904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8.64 Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of<BR>\n" );
document.write( "cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped<BR>\n" );
document.write( "kernels were counted. There were 86. (a) Construct a 90 percent confidence interval for the proportion<BR>\n" );
document.write( "of all kernels that would not pop. (b) Check the normality assumption. (c) Try the Very Quick<BR>\n" );
document.write( "Rule. Does it work well here? Why, or why not? (d) Why might this sample not be typical? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340303 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=340303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. <BR>\n" );
document.write( "(a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop.<BR>\n" );
document.write( "p-hat = 86/773 = 0.111..<BR>\n" );
document.write( "E = 1.645*sqrt[(0.111)(0.889)/773]=0.0186<BR>\n" );
document.write( "90% CI: 0.111-0.0186 < p < 0.111+0.0186<BR>\n" );
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document.write( "(b) Check the normality assumption<BR>\n" );
document.write( "I'll let you do that; it differs with every text.\r<BR>\n" );
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document.write( "(c) Try the Very Quick Rule.<BR>\n" );
document.write( "Does it work well here? Why, or why not?<BR>\n" );
document.write( "I'm not sure what that is; it depends on your text.<BR>\n" );
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document.write( "(d) Why might this sample not be typical?<BR>\n" );
document.write( "The 773 is probably not a simple-random-sample<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" );
document.write( "</TD></TR></TABLE>\n" );