document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201156>Question 1201156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, please i need help with this question. In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained:\r<BR>\n" );
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document.write( "Specimen: 1,2,3,4,5,6.<BR>\n" );
document.write( "A: 10.16,10.88,10.49,5.29,8.25,7.58<BR>\n" );
document.write( "B: 10.17,10.87,10.48,5.28,8.26,7.54\r<BR>\n" );
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document.write( "State the null and alternate hypotheses.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835418 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=835418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll provide the answers first at the top of the page.<BR>\n" );
document.write( "The next section will do a deeper dive explaining things.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<ul><li><font color=red>null hypothesis</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D+=+matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > aka <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D-matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29=+matrix%281%2C2%2C%22%22%2C0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><font color=red>alternate hypothesis</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D+%3C%3E+matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > aka <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D-matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29%3C%3E+matrix%281%2C2%2C%22%22%2C0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul>mu = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" > is used for the population mean.<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Standard practice with population parameters generally involves Greek letters.<BR>\n" );
document.write( "Examples:<ul><li>Greek letter mu = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population mean</li><li>Greek letter sigma = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma ALIGN=MIDDLE  ALT=\"sigma\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population standard deviation</li><li>Greek letter rho = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rho ALIGN=MIDDLE  ALT=\"rho\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population correlation coefficient</li></ul>and so on. We use the lowercase version of each letter.\r<BR>\n" );
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document.write( "The one exception to this rule, that I can think of anyway, is the use of 'p' for the population proportion (the sample version is phat). \r<BR>\n" );
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document.write( "We're looking at the mean weights so we go for mu or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Both \"mean\" and \"mu\" start with M, which is one way to remember the connection.\r<BR>\n" );
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document.write( "If we want to talk about two (or more) different population means, it's common to attach a number to the bottom right corner of this variable.<ul><li>mu1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2C1%29%5D ALIGN=MIDDLE  ALT=\"mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2C1%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population mean of group 1</li><li>mu2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2C2%29%5D ALIGN=MIDDLE  ALT=\"mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2C2%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population mean of group 2</li><li>etc</li></ul>Some textbooks will use letters instead of numbers.<ul><li>muA = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D ALIGN=MIDDLE  ALT=\"mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population mean of group A</li><li>muB = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population mean of group B</li><li>etc</li></ul>To be even more descriptive, the letters can be replaced with short names.<BR>\n" );
document.write( "Examples:<ul><li>mu_dogs = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2Cdogs%29%5D ALIGN=MIDDLE  ALT=\"mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2Cdogs%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population mean of dogs' weight</li><li>mu_cats = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2Ccats%29%5D ALIGN=MIDDLE  ALT=\"mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2Ccats%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = population mean of cats' weight</li></ul>It will depend on context which is the better format.<BR>\n" );
document.write( "Statistical software like Minitab often uses a format similar to the last set of examples shown above.\r<BR>\n" );
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document.write( "Since your teacher is involving letters, I'll go for that style. \r<BR>\n" );
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document.write( "The instructions mention \"<font color=blue>In an experiment to determine whether there is a systematic difference between the weights</font>\"<BR>\n" );
document.write( "Meaning that the researcher wants to test the claim if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D+%3C%3E+matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > is the case or not.<BR>\n" );
document.write( "The flip of that statement would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D+=+matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For each statement, we can optionally subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D ALIGN=MIDDLE  ALT=\"mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "Eg: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D+=+matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D-matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29=+matrix%281%2C2%2C%22%22%2C0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Why do we bother with this subtraction? It's to conduct a hypothesis test on the difference of the population means. <BR>\n" );
document.write( "Treat that difference as a new random variable on its own. \r<BR>\n" );
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document.write( "Rule: The null hypothesis <b><u>ALWAYS</u></b> has the equal sign. <BR>\n" );
document.write( "This is to lock the parameter(s) into one spot and set up one distribution.\r<BR>\n" );
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document.write( "Therefore,<ul><li><font color=red>null hypothesis</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D+=+matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > aka <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D-matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29=+matrix%281%2C2%2C%22%22%2C0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><font color=red>alternate hypothesis</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D+%3C%3E+matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > aka <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D-matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29%3C%3E+matrix%281%2C2%2C%22%22%2C0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul>This is a two-tailed test because of the \"not equals\" in the alternate/alternative hypothesis.\r<BR>\n" );
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document.write( "I'll stop here since it seems like all you need are the null and alternate hypotheses. <BR>\n" );
document.write( "Let me know if have further questions. Or please make a new post on this website.<BR>\n" );
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