document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141844>Question 141844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9.65 A consumer agency tested 290 hams, finding that 64 were underweight. (a) Construct a 95 percent<BR>\n" );
document.write( "confidence interval for the true percent of underweight hams. (b) If the goal is to reduce the incidence<BR>\n" );
document.write( "of underweight hams to 25 percent or less, does this sample show that the goal is being<BR>\n" );
document.write( "achieved? (c) Explain how this confidence interval is equivalent to a two-tailed test at &#945; = .05.<BR>\n" );
document.write( "(Data are from Detroit Free Press, March 9, 1999, p. 2A.)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103345 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=103345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A consumer agency tested 290 hams, finding that 64 were underweight. <BR>\n" );
document.write( "(a) Construct a 95 percent confidence interval for the true percent of underweight hams. <BR>\n" );
document.write( "p-hat = 64/290 = 0.22<BR>\n" );
document.write( "E = 1.96sqrt(0.22*0.78/290) = 0.024<BR>\n" );
document.write( "95% CI: 0.22-0.024 < p < 0.22+0.024<BR>\n" );
document.write( ": 0.196 < p <  0.22024\r<BR>\n" );
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document.write( "(b) If the goal is to reduce the incidence of under weight hams to 25 percent or less, does this sample show that the goal is being achieved? <BR>\n" );
document.write( "No, we have 95% confidence that p is between 19.6% and 22%<BR>\n" );
document.write( "That interval does not include 25%<BR>\n" );
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document.write( "(c) Explain how this confidence interval is equivalent to a two-tailed test at &#945; = .05.<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );