document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=458332>Question 458332</A>: <I><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 of the proportion of all kernels that would not pop.<BR>\n" );
document.write( "(b)	Check the normality assumption.<BR>\n" );
document.write( "(c)	Try the Very Quick Rule. Does it work well here? Why or why not?<BR>\n" );
document.write( "(d)	Why might this sample not be typical?<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 #314486 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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/cgi-bin/show-face.mpl?user=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=314486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From yahoo.com<BR>\n" );
document.write( "Best Answer - Chosen by Asker\r<BR>\n" );
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document.write( "We know N, the sample size, from the problem: N = 773<BR>\n" );
document.write( "From your problem's givens, we can get p and q:\r<BR>\n" );
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document.write( "p = 86/773 = 0.1113<BR>\n" );
document.write( "q = 1 - p = 0.8887\r<BR>\n" );
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document.write( "From a z table, the value for the 90% interval is:\r<BR>\n" );
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document.write( "1.6449\r<BR>\n" );
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document.write( "Use the formula for the interval around a proportion:\r<BR>\n" );
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document.write( "p - z*sqrt(pq/N) to p + z*sqrt(pq/N)\r<BR>\n" );
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document.write( "0.1113 - 1.6449*sqrt(0.1113*0.8887/773) to 0.1113 + 1.6449*sqrt(0.1113*0.8887/773)\r<BR>\n" );
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document.write( "0.09269 to 0.12991\r<BR>\n" );
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document.write( "No, the very quick rule won't work here, since the p value is very small.\r<BR>\n" );
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document.write( "Yes, normality will hold, since Np and Nq are both large (86 and 687).\r<BR>\n" );
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document.write( "This sample might not be typical, for example, since the person is a \"self-confessed connoisseur of cheap popcorn\", he might be better at making the popcorn than other people, so he might have a lower number of unpopped kernals than a normal eater.<BR>\n" );
document.write( "3 years ago </SPAN>\n" );
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