document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241546>Question 241546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)The times required by three workers to perform an assembly-line task were recorded on five randomly selected occasions. Here are the times, to the nearest minute.\r<BR>\n" );
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document.write( "Hank     	Joseph	     Susan	<BR>\n" );
document.write( "8	          8	      10	<BR>\n" );
document.write( "10	          9	       9	<BR>\n" );
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document.write( "9	          9	      10	<BR>\n" );
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document.write( "11	          8	      11	<BR>\n" );
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document.write( "10	         10	        9	\r<BR>\n" );
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document.write( "Assuming the normality of populations under consideration, at the 5% significance level,\r<BR>\n" );
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document.write( "do the data provide sufficient evidence to conclude that a difference exists between the times required by three workers to perform an assembly-line task?\r<BR>\n" );
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document.write( "2)240 students were asked to taste three types of cola in a random order and were not told their identity. The contingency table below shows the counts of preferred colas classified by the subject specialism of students.\r<BR>\n" );
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document.write( "Cola C	Cola B	Cola A	<BR>\n" );
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document.write( "44	23	13	Mathematics<BR>\n" );
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document.write( "10	24	36	Economics<BR>\n" );
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document.write( "8	8	24	Statistics<BR>\n" );
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document.write( "11	28	11	Management<BR>\n" );
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document.write( "Use These data to investigate the association, if any, between a student's subject specialism and preferred cola-type. Interpret any association which exists, testing at more than one significance level.\r<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 #176936 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=176936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The times required by three workers to perform an assembly-line task were recorded on five randomly selected occasions. Here are the times, to the nearest minute.\r<BR>\n" );
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document.write( "<BR>\n" );
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document.write( "Hank     	Joseph	     Susan	<BR>\n" );
document.write( "8	          8	      10	<BR>\n" );
document.write( "10	          9	       9	<BR>\n" );
document.write( "			<BR>\n" );
document.write( "9	          9	      10	<BR>\n" );
document.write( "	 		<BR>\n" );
document.write( "11	          8	      11	<BR>\n" );
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document.write( "10	         10	        9	\r<BR>\n" );
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document.write( "Assuming the normality of populations under consideration, at the 5% significance level,<BR>\n" );
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document.write( "Ho: The means are all equal<BR>\n" );
document.write( "H1: At least one of the means is different<BR>\n" );
document.write( "I ran an ANOVA test on the data and got the following results:<BR>\n" );
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document.write( "test statistic: F= 1.2653...<BR>\n" );
document.write( "p-value = 0.3172<BR>\n" );
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document.write( "Conclusion: Since the p-value is greater than 5%, do not reject Ho.<BR>\n" );
document.write( "At the 5% significance level the means are equal.<BR>\n" );
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document.write( "Do the data provide sufficient evidence to conclude that a difference exists between the times required by three workers to perform an assembly-line task?\r<BR>\n" );
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document.write( "2)240 students were asked to taste three types of cola in a random order and were not told their identity. The contingency table below shows the counts of preferred colas classified by the subject specialism of students.\r<BR>\n" );
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document.write( "Cola C	Cola B	Cola A	<BR>\n" );
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document.write( "44	23	13	Mathematics<BR>\n" );
document.write( "			<BR>\n" );
document.write( "10	24	36	Economics<BR>\n" );
document.write( "			<BR>\n" );
document.write( "8	8	24	Statistics<BR>\n" );
document.write( "			<BR>\n" );
document.write( "11	28	11	Management<BR>\n" );
document.write( "			<BR>\n" );
document.write( "Use These data to investigate the association, if any, between a student's subject specialism and preferred cola-type. Interpret any association which exists, testing at more than one significance level.<BR>\n" );
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document.write( "Ho: The row and column factors are independent<BR>\n" );
document.write( "H1: They are not independent<BR>\n" );
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document.write( "I ran a Chi-Sq test on the data and got the following:<BR>\n" );
document.write( "test stat: Chi-Sq = 32.39..<BR>\n" );
document.write( "p-value = 0.00000159...<BR>\n" );
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document.write( "Conclusion: Since the p-value is less than 1% reject Ho at the 1% significance<BR>\n" );
document.write( "level. The row and column factors are not independent.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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