document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=339300>Question 339300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. A watch manufacturer creates watch springs whose properties must be consistent.  In particular, the standard deviation in their weights must be no greater than 3.0 grams.  Fifteen watch springs are selected from the production line and measured; their weights are 2, 4, 10, 10, 8, 8, 9, 10, 9, 5, 3, 2, 4, 2, and 2 grams.  Assume  = 0.01.<BR>\n" );
document.write( "· State the null and alternate hypotheses<BR>\n" );
document.write( "· Calculate the sample standard deviation<BR>\n" );
document.write( "· Determine which test statistic is appropriate (chi-square or F), and calculate its value.<BR>\n" );
document.write( "· Determine the critical value(s).<BR>\n" );
document.write( "· State your decision: Should the null hypothesis be rejected? <BR>\n" );
document.write( "(Points :10)\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 #243177 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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/cgi-bin/show-face.mpl?user=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=243177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> · State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma=3 ALIGN=MIDDLE  ALT=\"sigma=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ha: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%3C3 ALIGN=MIDDLE  ALT=\"sigma%3C3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "· Calculate the sample standard deviation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=3.335 ALIGN=MIDDLE  ALT=\"s=3.335\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "· Determine which test statistic is appropriate (chi-square or F), and calculate its value.<BR>\n" );
document.write( "test statistic:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-1%29%2AS%5E2%2F%28sigma%5B0%5D%29%5E2=%2815-1%29%2A3.335%5E2%2F3%5E2=17.30 ALIGN=MIDDLE  ALT=\"%28n-1%29%2AS%5E2%2F%28sigma%5B0%5D%29%5E2=%2815-1%29%2A3.335%5E2%2F3%5E2=17.30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "· Determine the critical value(s).<BR>\n" );
document.write( "lower tail <BR>\n" );
document.write( "Chi^2 (1-alpha, dof)=chi^2(0.99,14)=4.66<BR>\n" );
document.write( "---<BR>\n" );
document.write( "· State your decision: Should the null hypothesis be rejected? <BR>\n" );
document.write( "since test statistic=17.30>critical value=4.66 cannot reject Ho.<BR>\n" );
document.write( "Conclusion:  No evidence against <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma=3 ALIGN=MIDDLE  ALT=\"sigma=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );