document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235409>Question 235409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need your help in working this problem out. Thank you very much... \r<BR>\n" );
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document.write( "A watch manufacturer creates watch springs whose properties must be consistent.  In particular, the standard deviation in their weights must be no greater than 2.0 grams.  Fifteen watch springs are selected from the production line and measured; their weights are 1, 4, 8, 7, 1, 5, 1, 4, 1, 4, 3, 9, 1, 3, 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173654 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=173654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A watch manufacturer creates watch springs whose properties must be consistent. In particular, the standard deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 1, 4, 8, 7, 1, 5, 1, 4, 1, 4, 3, 9, 1, 3, and 2 grams. Assume = 0.01.<BR>\n" );
document.write( "· State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: sigma^2 <= 4 (claim)<BR>\n" );
document.write( "Ha: sigma^2 > 4 <BR>\n" );
document.write( "· Calculate the sample standard deviation<BR>\n" );
document.write( "std of the sample = 2.667<BR>\n" );
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document.write( "· Determine which test statistic is appropriate (chi-square or F), and calculate its value.<BR>\n" );
document.write( "Chi-Sq = (n-1)*s^2/sigma^2 = 14*2.667^2/4 = 24.895<BR>\n" );
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document.write( "· Determine the critical value(s)<BR>\n" );
document.write( "Chi-Sq lower = 4.075  ; Chi-Sq upper = 31.32<BR>\n" );
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document.write( "State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( "Since the ts is not in either rejection interval, do not<BR>\n" );
document.write( "reject Ho based on these test results.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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