document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064093>Question 1064093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can some please show me how to use the chi-squared distribution to test the hypothesis of this problem?\r<BR>\n" );
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document.write( "A restaurant owner wants to see if the business is good enough for him to purchase a restaurant. He asks the present owner for a breakdown of how many customers that come in for lunch each day and the results are as follows: Monday - 20, Tuesday - 30, Wednesday - 25, Thursday - 40 and Friday - 55. The prospective owner observes the restaurant and finds the following number of customers coming for lunch each day: Monday- 30, Tuesday - 15, Wednesday- 7, Thursday 40, and Friday - 33. At a 95% confidence level determine whether the present owner reported the correct number of customers for lunch each day.\r<BR>\n" );
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document.write( "Thank you in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679209 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=679209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> restaurant owner's sample is 20+30+25+40+55 = 170<BR>\n" );
document.write( "p1 = 20/170 = 0.12 for Monday<BR>\n" );
document.write( "p2 = 30/170 = 0.18 for Tuesday<BR>\n" );
document.write( "p3 = 25/170 = 0.15 for Wednesday<BR>\n" );
document.write( "p4 = 40/170 = 0.23 for Thursday<BR>\n" );
document.write( "p5 = 55/170 = 0.32 for Friday<BR>\n" );
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document.write( "prospective owner's sample is 30+15+7+40+33 = 125<BR>\n" );
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document.write( "H0: The distribution of the prospective owners sample is 0.12, 0.18, 0.15, 0.23, 0.32<BR>\n" );
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document.write( "H1: H0 is false<BR>\n" );
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document.write( "strictly speaking in order to use chi-squared distribution we must check for<BR>\n" );
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document.write( "min(0.12(125) +0.18(125), 0.15(125), 0.23(125), 0.32(125)) > 5<BR>\n" );
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document.write( "min(15, 22, 19, 29, 40) > 5, yes since 15 > 5<BR>\n" );
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document.write( "degrees of freedom = 5 - 1 = 4 and a 95% confidence level<BR>\n" );
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document.write( "the X^2 table for 4 degrees of freedom and a = 0.05 ( 1 - 95/100)<BR>\n" );
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document.write( "the critical value is 9.49<BR>\n" );
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document.write( "we reject H0 if X^2 > or = 9.49<BR>\n" );
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document.write( "X^2 = summation from 1 to 5 ( observed value - expected value)^2 / expected value<BR>\n" );
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document.write( "Note the expected values are (15, 22, 19, 29, 40) and observed values are (30, 15, 7, 40, 33)<BR>\n" );
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document.write( "X^2 = 30.02<BR>\n" );
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document.write( "we reject H0 - the owner did not report the correct number of customers<BR>\n" );
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