document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=574039>Question 574039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new television series must show that it has at least 25% of the viewing audience after its initial 13- week run, in order to be judged successful. In a sample of 400 households, 112 were watching the series. At a 5% significance level, would the series be judged successful on the basis of this sample information? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368955 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=368955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A new television series must show that it has at least 25% of the viewing audience after its initial 13- week run, in order to be judged successful. In a sample of 400 households, 112 were watching the series. At a 5% significance level, would the series be judged successful on the basis of this sample information?<BR>\n" );
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document.write( "Ho: p >= 0.25<BR>\n" );
document.write( "Ha: p < 0.25<BR>\n" );
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document.write( "sample proportion: p-hat = (112/400) = 0.28<BR>\n" );
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document.write( "z(0.28) = (0.28-0.25)/sqrt[0.25*0.75/400] = 1.3856<BR>\n" );
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document.write( "p-value = P(z > 1.3856) = normalcdf(1.3856,100) = 0.0829<BR>\n" );
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document.write( "Conclusion: since the p-value > 5%, fail to reject Ho.<BR>\n" );
document.write( "The test results support the success of the TV series.<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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