document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146428>Question 146428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a three-digit lottery, each of the three digits is supposed to have the same probability of occurrence<BR>\n" );
document.write( "(counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency<BR>\n" );
document.write( "of occurrence of each digit for 90 consecutive daily three-digit drawings. (a) Make a bar chart and<BR>\n" );
document.write( "describe it. (b) Calculate expected frequencies for each class. (c) Perform the chi-square test for a<BR>\n" );
document.write( "uniform distribution. At &#945; = .05, can you reject the hypothesis that the digits are from a uniform<BR>\n" );
document.write( "population? Lottery3<BR>\n" );
document.write( "Digit Frequency<BR>\n" );
document.write( "0 33<BR>\n" );
document.write( "1 17<BR>\n" );
document.write( "2 25<BR>\n" );
document.write( "3 30<BR>\n" );
document.write( "4 31<BR>\n" );
document.write( "5 28<BR>\n" );
document.write( "6 24<BR>\n" );
document.write( "7 25<BR>\n" );
document.write( "8 32<BR>\n" );
document.write( "9 25<BR>\n" );
document.write( "Total 270 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106976 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=106976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a three-digit lottery, each of the three digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). <BR>\n" );
document.write( "The table shows the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings. <BR>\n" );
document.write( "(a) Make a bar chart and describe it.<BR>\n" );
document.write( "Can't do that on this site.<BR>\n" );
document.write( "------------------------------------ <BR>\n" );
document.write( "(b) Calculate expected frequencies for each class.<BR>\n" );
document.write( "270/10 = 27 for each digit<BR>\n" );
document.write( "---------------------------------- <BR>\n" );
document.write( "(c) Perform the chi-square test for a uniform distribution. <BR>\n" );
document.write( "At &#945; = .05, can you reject the hypothesis that the digits are from a uniform<BR>\n" );
document.write( "population?<BR>\n" );
document.write( "chi-Sq = 4.16<BR>\n" );
document.write( "p-value = 0.9<BR>\n" );
document.write( "Conclusion: Since the p-value is greater than 5%, reject the null hypothesis which states that the distribution is uniform.<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "Lottery3<BR>\n" );
document.write( "Digit Frequency<BR>\n" );
document.write( "0 33<BR>\n" );
document.write( "1 17<BR>\n" );
document.write( "2 25<BR>\n" );
document.write( "3 30<BR>\n" );
document.write( "4 31<BR>\n" );
document.write( "5 28<BR>\n" );
document.write( "6 24<BR>\n" );
document.write( "7 25<BR>\n" );
document.write( "8 32<BR>\n" );
document.write( "9 25<BR>\n" );
document.write( "Total 270<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );