document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175474>Question 1175474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Test the claim that the proportion of people who own cats is smaller than 90% at the 0.01 significance level. The null and alternative hypothesis would be:<BR>\n" );
document.write( "H0:p≥0.9<BR>\n" );
document.write( "H1:p<0.9<BR>\n" );
document.write( "Based on a sample of 500 people, 83% owned cats<BR>\n" );
document.write( "What is The test statistic is: (2 decimal places)<BR>\n" );
document.write( "The p value (2 decimal places).\r<BR>\n" );
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document.write( "2. You wish to test the following claim ( Ha ) at a significance level of  α= 0.001.\r<BR>\n" );
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document.write( "Ho:p=0.61<BR>\n" );
document.write( "Ha:p>0.61<BR>\n" );
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document.write( "You obtain a sample of size n= 382 in which there are 240 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) The p-value for this test is (assuming  Ho is true) the probability of observing... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801848 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming randomness etc.<BR>\n" );
document.write( "test stat is a z=(p hat-p)/sqrt(p*(1-p)/n)<BR>\n" );
document.write( "Critical value is z< -2.33<BR>\n" );
document.write( "=-.07/sqrt(.9*.1/500)<BR>\n" );
document.write( "=.-.07/0.013<BR>\n" );
document.write( "=-5.21<BR>\n" );
document.write( "reject Ho<BR>\n" );
document.write( "p-value <0.0001 (4 x 10^(-7)<BR>\n" );
document.write( "Note: realistically have to use 416 or 417 for the numerator of the proportion since 83% of 500 is not an integer. It doesn't change the answer.\r<BR>\n" );
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document.write( "Probability is 0.2490 that it is >0.61. (0.7510 that it is 239 or fewer)<BR>\n" );
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document.write( "check with the normal approximation, which ought to be about this.\r<BR>\n" );
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document.write( "np=mean or 233.02<BR>\n" );
document.write( "np(1-p)=variance or 90.8778 <BR>\n" );
document.write( "sd is sqrt(V)=9.53<BR>\n" );
document.write( "z>(239.5-233.02/9.53  which is 6.48/9.53 or z > 0.68 which is prob. 0.2482<BR>\n" );
document.write( "Use the answer above of 0.2490.<BR>\n" );
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