document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269315>Question 269315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "An insurance company states that 75% of its claims are settled within 5 weeks.  A consumer group selected a random sample of 25 of the company’s claims and found 8 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group’s claim that fewer than 75% of the claims were settled within 5 weeks?  Test using the traditional approach with &#945; = 0.05.<BR>\n" );
document.write( "·         State the null and alternate hypotheses<BR>\n" );
document.write( "·         Calculate the sample proportion<BR>\n" );
document.write( "·         Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "·         Determine the critical value(s).<BR>\n" );
document.write( "·         State your decision: Should the null hypothesis be rejected?\r<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 #197447 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=197447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An insurance company states that 75% of its claims are settled within 5 weeks.<BR>\n" );
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document.write( "A consumer group selected a random sample of 25 of the company’s claims and found 8 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 75% of the claims were settled within 5 weeks? Test using the traditional approach with &#945; = 0.05.<BR>\n" );
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document.write( "· State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: p >= 0.75<BR>\n" );
document.write( "H1: p < 0.75<BR>\n" );
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document.write( "· Calculate the sample proportion<BR>\n" );
document.write( "p-hat = 8/25 = 0.32<BR>\n" );
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document.write( "· Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "z(0.32) + (0.32 - 0.75)/sqrt[0.75*0.25/75] = -8.6<BR>\n" );
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document.write( "· Determine the critical value for left-tail test with alpha = 5%<BR>\n" );
document.write( "= invNorm(0.05) = -1.645<BR>\n" );
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document.write( "· State your decision: Should the null hypothesis be rejected? <BR>\n" );
document.write( "Since the cv is not in the rejection interval, fail to reject Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );