document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171917>Question 1171917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me. This is a hypothesis testing problem. Professor Jennings claims that only 36% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 86 students shows that 33 have jobs. Do the data indicate that less than 36% of the students have jobs? Use ∝ = 0.05. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796845 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=796845\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: p >=0.36<BR>\n" );
document.write( "Ha: p < 0.36<BR>\n" );
document.write( "alpha=0.05 p{reject Ho|Ho true}<BR>\n" );
document.write( "One way test.<BR>\n" );
document.write( "critical value is z < -1.645<BR>\n" );
document.write( "z=(phat-p)/sqrt(p(1-p)/n)<BR>\n" );
document.write( "33/86=0.384<BR>\n" );
document.write( "Right there, the evidence is sufficient not to reject Ho, since the sample proportion is greater than 36%.<BR>\n" );
document.write( "z=(0.384-0.36)/sqrt(0.36*0.64/86)<BR>\n" );
document.write( "=0.46<BR>\n" );
document.write( "This is obviously greater than -1.645 so fail to reject Ho<BR>\n" );
document.write( "p-value =0.65<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Note, if it is to be proven that MORE than 36% have jobs (some implication by how the question was asked, that there was concern there were more than 36% working, not fewer), then Ho is p < =0.36 and Ha:p >0.36<BR>\n" );
document.write( "and the critical value is z > 1.645.<BR>\n" );
document.write( "Still fail to reject in this instance, in that the proportion of 38.4% of students working is within the margin of error with z not >1.645 and p-value 0.32. </SPAN>\n" );
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