document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179289>Question 1179289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following calculate the test statistic, If convenient, use technology:\r<BR>\n" );
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document.write( "a=0.10\r<BR>\n" );
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document.write( "Type of worker     Professional    Personal    Both<BR>\n" );
document.write( "Technical            38               35        34<BR>\n" );
document.write( "Other                49               30        34 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850247 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To calculate the test statistic for this contingency table, we will use the chi-square test for independence.\r<BR>\n" );
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document.write( "1. Set up the Hypothesis:\r<BR>\n" );
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document.write( "Null Hypothesis (H0): The type of worker and the category (Professional, Personal, Both) are independent.<BR>\n" );
document.write( "Alternative Hypothesis (H1): The type of worker and the category are dependent.<BR>\n" );
document.write( "2. Create the Contingency Table:\r<BR>\n" );
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document.write( "Type of Worker	Professional	Personal	Both	Total<BR>\n" );
document.write( "Technical	38	35	34	107<BR>\n" );
document.write( "Other	49	30	34	113<BR>\n" );
document.write( "Total	87	65	68	220\r<BR>\n" );
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document.write( "Export to Sheets<BR>\n" );
document.write( "3. Calculate the Expected Frequencies:\r<BR>\n" );
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document.write( "The expected frequency for each cell is calculated as:\r<BR>\n" );
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document.write( "Expected Frequency = (Row Total * Column Total) / Grand Total\r<BR>\n" );
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document.write( "Expected (Technical, Professional) = (107 * 87) / 220 ≈ 42.34<BR>\n" );
document.write( "Expected (Technical, Personal) = (107 * 65) / 220 ≈ 31.65<BR>\n" );
document.write( "Expected (Technical, Both) = (107 * 68) / 220 ≈ 33.01<BR>\n" );
document.write( "Expected (Other, Professional) = (113 * 87) / 220 ≈ 44.66<BR>\n" );
document.write( "Expected (Other, Personal) = (113 * 65) / 220 ≈ 33.35<BR>\n" );
document.write( "Expected (Other, Both) = (113 * 68) / 220 ≈ 34.99<BR>\n" );
document.write( "4. Calculate the Chi-Square Statistic:\r<BR>\n" );
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document.write( "The chi-square statistic (χ²) is calculated using the formula:\r<BR>\n" );
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document.write( "χ² = Σ [(Observed - Expected)² / Expected]\r<BR>\n" );
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document.write( "χ² = [(38 - 42.34)² / 42.34] + [(35 - 31.65)² / 31.65] + [(34 - 33.01)² / 33.01] + [(49 - 44.66)² / 44.66] + [(30 - 33.35)² / 33.35] + [(34 - 34.99)² / 34.99]\r<BR>\n" );
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document.write( "χ² ≈ 0.457 + 0.354 + 0.029 + 0.413 + 0.334 + 0.028\r<BR>\n" );
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document.write( "χ² ≈ 1.615\r<BR>\n" );
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document.write( "Using Technology:\r<BR>\n" );
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document.write( "As shown by the provided python code, using the scipy library the chi-square statistic is calculated as 1.612983358368212.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "The test statistic (chi-square statistic) is approximately 1.613. </SPAN>\n" );
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