document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176058>Question 176058</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 $2.14. The means appear to be very close, but not the variances. At &#945; = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule. (Data are from a project by statistics students Kim Dyer, Amy Pease, and Lyndsey Smith.)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134550 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=134550\">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 &#945; = .05, 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: variance matinee = variance evening<BR>\n" );
document.write( "Ha: they are not equal<BR>\n" );
document.write( "Run 2-Sample F-Test to get:<BR>\n" );
document.write( "Test Stat: F = 1.9915...<BR>\n" );
document.write( "p-value: 0.09811...<BR>\n" );
document.write( "df numerator = 24 = df denominator<BR>\n" );
document.write( "Critical Value: F(right) = 2.23 ; F(left)= 1/2.33 = 0.448..<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Conclusion: Since p-value is greater than 5%, Fail to reject Ho.<BR>\n" );
document.write( "The variances are not statistically different.<BR>\n" );
document.write( "=================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );