document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115731>Question 1115731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a Harris&#8203; poll, adults were asked if they are in favor of abolishing the penny.  Among the&#8203; responses, 1222 answered&#8203; \"no,\" 458 answered&#8203; \"yes,\" and 366 had no opinion.  What is the sample proportion of yes&#8203; responses, and what notation is used to represent&#8203; it?<BR>\n" );
document.write( "Choose the correct answer below.<BR>\n" );
document.write( "A. ModifyingAbove p with caretequals 0.224.  The symbol ModifyingAbove p with caret is used to represent a sample proportion.<BR>\n" );
document.write( "B. pequals0.224.  The symbol p is used to represent a sample proportion.<BR>\n" );
document.write( "C. ModifyingAbove p with caretequals 0.273.  The symbol ModifyingAbove p with caret is used to represent a sample proportion.<BR>\n" );
document.write( "D. p equals 0.273.  The symbol p is used to represent a sample proportion. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #730555 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=730555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "The letter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > without any special markings over it represents the population proportion\r<BR>\n" );
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document.write( "While the notation <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \hat{p}\"> is known as \"p-hat\", or as your book/teacher describes \"p with caret\". The caret symbol is <font color=blue size=5>^</font> which rests on top of the letter p, as if p was wearing the caret as a hat.\r<BR>\n" );
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document.write( "The symbol p-hat is used for sample proportions. <BR>\n" );
document.write( "The formula to compute p-hat is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \hat{p} = \frac{x}{n}\"><BR>\n" );
document.write( "where<BR>\n" );
document.write( "x = number of successes (in this case, we want the number of \"yes\" responses)<BR>\n" );
document.write( "n = sample size\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "x = 458 \"yes\" responses<BR>\n" );
document.write( "n = 2046 because we add up the values 1222+458+366 for \"no\", \"yes\", and \"no opinion\" respectively\r<BR>\n" );
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document.write( "So the value of p-hat is approximately...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \hat{p} = \frac{x}{n}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \hat{p} = \frac{458}{2046}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \hat{p} \approx 0.2238514\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \hat{p} \approx 0.224\"><BR>\n" );
document.write( "Making the <font color=red size=4>final answer to be choice A</font> \r<BR>\n" );
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document.write( "Choice B is not the answer because we use p-hat instead of p. <BR>\n" );
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