document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=542707>Question 542707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $1.98. The means appear to be very close, but not the variances. At &#945; = .03, is there a difference in variances?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354697 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=354697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At the .05 level of significance, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Ho: s^2(matinee)=s^2(evening)<BR>\n" );
document.write( "Ha: s^2(matinee) is not equal to s^2(evening)<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Two-tailed test with alpha = 0.05<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Test Statistic: F = (2.14)^2/(3.02)^2 = 0.502127<BR>\n" );
document.write( "-------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Critical Value:<BR>\n" );
document.write( "numerator df's = 24 ; denominator df's = 24<BR>\n" );
document.write( "F = 2.27<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Conclusion:<BR>\n" );
document.write( "Since the Test Statistic is less than the Critical Value, Fail to <BR>\n" );
document.write( "reject Ho.<BR>\n" );
document.write( "The variances for matinee and evening are statistically equivalent.<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );