document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193955>Question 1193955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in <BR>\n" );
document.write( "the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to <BR>\n" );
document.write( "have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans. At the 0.05 <BR>\n" );
document.write( "level of significance. Which test will be used to test the hypothesis that <BR>\n" );
document.write( "the machine is mixing the nuts in the ratio 5:2:2:1. State the Null and <BR>\n" );
document.write( "Alternative hypothesis.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848548 by </B><A HREF=/tutors/aboutme.mpl?userid=parmen><B>parmen(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=parmen><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=848548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **Test to be used:**\r<BR>\n" );
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document.write( "The appropriate test for this scenario is the **Chi-Square Goodness-of-Fit Test**. This test is used to determine if the observed frequencies of different categories in a sample significantly differ from the expected frequencies under a specific hypothesis.\r<BR>\n" );
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document.write( "**Null and Alternative Hypotheses:**\r<BR>\n" );
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document.write( "* **Null Hypothesis (H0):** The machine is mixing the nuts in the expected ratio of 5:2:2:1. <BR>\n" );
document.write( "* **Alternative Hypothesis (H1):** The machine is not mixing the nuts in the expected ratio of 5:2:2:1.\r<BR>\n" );
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document.write( "**In essence:**\r<BR>\n" );
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document.write( "* The null hypothesis states that the observed frequencies of peanuts, hazelnuts, cashews, and pecans in the can are consistent with the expected ratio.<BR>\n" );
document.write( "* The alternative hypothesis states that the observed frequencies are significantly different from the expected ratio, suggesting that the machine is not mixing the nuts correctly.<BR>\n" );
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