document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=304872>Question 304872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a sample of 100 Planter’s Mixed Nuts, 19 were found to be almonds. (a) Construct a 90 percent confidence interval for the true proportion of almonds. (b) May normality be assumed? Explain.<BR>\n" );
document.write( "(c) What sample size would be needed for 90 percent confidence and an error of ± 0.03? (d) Why would a quality control manager at Planter’s need to understand sampling? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218343 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=218343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a sample of 100 Planter’s Mixed Nuts, 19 were found to be almonds. <BR>\n" );
document.write( "(a) Construct a 90 percent confidence interval for the true proportion of almonds.<BR>\n" );
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document.write( "p-hat = 0.19<BR>\n" );
document.write( "standard error = 1.645*sqrt(0.19*0.81/100) = 0.0645<BR>\n" );
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document.write( "90% CI: 0.19-0.0645 < p < 0.19+0.0645<BR>\n" );
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document.write( "(b) May normality be assumed? Explain.<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
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document.write( "(c) What sample size would be needed for 90 percent confidence and an error of ± 0.03? <BR>\n" );
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document.write( "n = [z/E]^2*pq<BR>\n" );
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document.write( "n = [1.645/0.03]^2*0.19*0.81 = 462.65<BR>\n" );
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document.write( "Round up to n = 463<BR>\n" );
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document.write( "(d) Why would a quality control manager at Planter’s need to understand sampling?<BR>\n" );
document.write( "Testing will show him whether the product is as it is being advertised.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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