document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67802>Question 67802</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0471656828/algebrahomeworkh>Statistics Principles and Methods</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble with calculating p-values.  I have two problems that I just can't figure out.  This is the first:<BR>\n" );
document.write( "A survey of 120 high school students shows that 39 of them work over 20 hours per week during the school year. Does it demonstrate the conjecture that more than 25% of the high school students work over 20 hours per week during the school year? (Answer by calculating the P-value.)\r<BR>\n" );
document.write( "\n" );
document.write( "I started out calculating the sample proportion:\r<BR>\n" );
document.write( "\n" );
document.write( "p^ = x / n = 39/120 = 0.325\r<BR>\n" );
document.write( "\n" );
document.write( "which means that 32.5 % work more than 20 hrs. per week, which is more than 25%, but how do you show that by calculating the P-value?  I tried to figure out the test statistic, but got lost.  Thanks for any help you can give.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48205 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=48205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A survey of 120 high school students shows that 39 of them work over 20 hours per week during the school year. Does it demonstrate the conjecture that more than 25% of the high school students work over 20 hours per week during the school year? (Answer by calculating the P-value.)\r<BR>\n" );
document.write( "\n" );
document.write( "I started out calculating the sample proportion:\r<BR>\n" );
document.write( "\n" );
document.write( "p^ = x / n = 39/120 = 0.325\r<BR>\n" );
document.write( "\n" );
document.write( "which means that 32.5 % work more than 20 hrs. per week, which is more than 25%, but how do you show that by calculating the P-value?  I tried to figure out the test statistic, but got lost.  Thanks for any help you can give.<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Ho:p=0.25<BR>\n" );
document.write( "Ha:p>0.25<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "You figured p-hat=0.325<BR>\n" );
document.write( "The test statistic is the following z-value.<BR>\n" );
document.write( "z(0.325)=(0.325-0.25)/sqrt[(0.325*0.675)/120]<BR>\n" );
document.write( "=0.075/0.042756=1.7541<BR>\n" );
document.write( "Draw a normal curve; label the horizontal axis as \"z\";<BR>\n" );
document.write( "mark \"0\" as the mean; put a point at 1.7541;<BR>\n" );
document.write( "Calculate the amount of area to the right of 1.7541 as<BR>\n" );
document.write( "0.0397066<BR>\n" );
document.write( "This is the p-value you are looking for.<BR>\n" );
document.write( "This p-value means there is approximately a 4% chance<BR>\n" );
document.write( "that the test proportion (0.325) could be higher than<BR>\n" );
document.write( "the proportion seen in the sample.  That is quite low<BR>\n" );
document.write( "and would result in rejecting Ho which said the population<BR>\n" );
document.write( "proportion was 0.25.  It probably is higher.<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );