document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250277>Question 250277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An insurance company states that 85% of its claims are settled within 5 weeks.  A consumer group selected a random sample of 50 of the company’s claims and found 21 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group’s claim that fewer than 85% of the claims were settled within 5 weeks?  Test using the traditional approach with &#945; = 0.02.<BR>\n" );
document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;State the null and alternate hypotheses<BR>\n" );
document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;Calculate the sample proportion <BR>\n" );
document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;Determine the critical value(s).<BR>\n" );
document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;State your decision: Should the null hypothesis be rejected?<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 #182211 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=182211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An insurance company states that 85% of its claims are settled within 5 weeks. <BR>\n" );
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document.write( "A consumer group selected a random sample of 50 of the company’s claims and found 21 of the claims were settled within 5 weeks. <BR>\n" );
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document.write( "Is there enough evidence to support the consumer group’s claim that fewer than 85% of the claims were settled within 5 weeks? <BR>\n" );
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document.write( "Test using the traditional approach with &#945; = 0.02.<BR>\n" );
document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: p = 0.85<BR>\n" );
document.write( "H1: p < 0.85<BR>\n" );
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document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;Calculate the sample proportion<BR>\n" );
document.write( "p-hat = 21/50 = 0.42<BR>\n" );
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document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "z(0.42) = (0.42-0.85)/sqrt(0.85*0.15/sqrt(50) = -3.2023<BR>\n" );
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document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;Determine the critical value(s).<BR>\n" );
document.write( "Assuming alpha = 5%, crit value for left tail test = invNorm(0.05) = -1.645<BR>\n" );
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document.write( "•&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61600;&#61472;State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( "Since the test stat is in the reject interval, reject Ho.<BR>\n" );
document.write( "Reject Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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