document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981117>Question 981117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lily Energy Systems manufacturer's wood-burning heaters and fireplace inserts. One of its systems has<BR>\n" );
document.write( "an electric blower, which is thermostatically controlled. The blower is designed to automatically turn on<BR>\n" );
document.write( "when the temperature in the stove reaches 125°F and turn off at 85°F. Complaints from customers indicate<BR>\n" );
document.write( "that the thermostat control is not working properly. The company feels that the thermostat is acceptable if<BR>\n" );
document.write( "the variance in the cutoff temperature is less than or equal to 175. The company takes a sample of 24<BR>\n" );
document.write( "thermostats and finds that the variance equals 289. The calculated chi-square test statistic and the table<BR>\n" );
document.write( "value for a 0.05 significance level are<BR>\n" );
document.write( "A. 37.983, 38.076.<BR>\n" );
document.write( "B. 35.172, 38.99.<BR>\n" );
document.write( "C. 37.983, 35.172.<BR>\n" );
document.write( "D. 38.076, 38.99. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602202 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=602202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hypothesis:<BR>\n" );
document.write( "Ho: sigma^2 <= 175<BR>\n" );
document.write( "Ha: sigma^2 > 175\r<BR>\n" );
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document.write( "This is a right tailed test. If the chi-square test statistic is larger than the cutoff critical value, then reject the null.\r<BR>\n" );
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document.write( "Test Statistic:<BR>\n" );
document.write( "[(n-1)*s^2]/(sigma^2)<BR>\n" );
document.write( "[(24-1)*289]/(175)<BR>\n" );
document.write( "37.9828571428571<BR>\n" );
document.write( "37.983\r<BR>\n" );
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document.write( "The chi-square test statistic is approximately <font color=\"red\">37.983</font>\r<BR>\n" );
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document.write( "To find the critical value, use a table like <a  rel=nofollow HREF=\"http://sites.stat.psu.edu/~mga/401/tables/Chi-square-table.pdf\">this one</a>. Look at the row that corresponds to df = n-1 = 24-1 = 23. Then look at the column that corresponds to the right tail having an area of 0.050. The value in this row/column intersection is 35.172\r<BR>\n" );
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document.write( "Critical value: <font color=\"red\">35.172</font>\r<BR>\n" );
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document.write( "Because the test statistic is larger than the critical value, we reject the null. We conclude that the variance is definitely larger than 175. So the company will have to fix the issue.<BR>\n" );
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