document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143410>Question 1143410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the conclusion whether or not to REJECT or FAIL TO REJECT the null hypotheses.<BR>\n" );
document.write( "The original claim: The percentage of of M&Ms is greater than 5%. The hypothesis test results in a p-value of 0.0010.<BR>\n" );
document.write( "alpha= 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 #764542 by </B><A HREF=/tutors/aboutme.mpl?userid=Velo><B>Velo(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Velo><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=764542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b>Hypothesis Testing using P-value:</b>\r<BR>\n" );
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document.write( "<b>Given</b>\r<BR>\n" );
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document.write( "Claim = M&Ms greater than 5%\r<BR>\n" );
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document.write( "P-value = 0.0010\r<BR>\n" );
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document.write( "alpha = 0.05\r<BR>\n" );
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document.write( "To make things easier, convert the percentage (P) of M&Ms from 5% to decimal form 0.05.\r<BR>\n" );
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document.write( "Therefore, M&Ms percentage shall be represented as follows: P > 0.05. \r<BR>\n" );
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document.write( "Next we state the hypotheses,\r<BR>\n" );
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document.write( "<b>Null Hypothesis</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H_0%3A+P+=+0.05 ALIGN=MIDDLE  ALT=\"H_0%3A+P+=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<b>Alternative hypothesis</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H_A%3A+P+%3E+0.05 ALIGN=MIDDLE  ALT=\"H_A%3A+P+%3E+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<b>Conclusion</b><BR>\n" );
document.write( "Since the P-value = 0.0010 is less than alpha of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+=+0.05 ALIGN=MIDDLE  ALT=\"alpha+=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we REJECT the null hypothesis, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H_0 ALIGN=MIDDLE  ALT=\"H_0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and conclude that the percentage of M&Ms is greater than 5%. Thus, the result is statistically significant.\r<BR>\n" );
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document.write( "<b>Also, the conclusion can be stated another way:</b>\r<BR>\n" );
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document.write( "Because alpha = 0.05 or 1 - 0.05 = 0.95\r<BR>\n" );
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document.write( "<b>Conclusion:</b> \"We are 95% confident that the percentage of M&Ms is greater than 5%\".</p>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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