document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193978>Question 1193978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The human resource director is concerned about absenteeism among hourly workers. She decides to sample the records to<BR>\n" );
document.write( "determine whether absenteeism is distributed evenly throughout the six-day workweek. Is absenteeism distributed evenly<BR>\n" );
document.write( "throughout the week? Use 0.01 level of significance. What is the decision regarding the null hypothesis? Specifically, what does<BR>\n" );
document.write( "this indicate to the human resources director?\r<BR>\n" );
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document.write( "          Number of absent<BR>\n" );
document.write( "Monday.   12<BR>\n" );
document.write( "Tuesday.   9<BR>\n" );
document.write( "Wednesday.11<BR>\n" );
document.write( "Thursday. 10<BR>\n" );
document.write( "Friday.   9<BR>\n" );
document.write( "Saturday. 9<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848543 by </B><A HREF=/tutors/aboutme.mpl?userid=parmen><B>parmen(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=parmen><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=848543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Set up Hypotheses**\r<BR>\n" );
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document.write( "* **Null Hypothesis (H0):** Absenteeism is evenly distributed throughout the workweek. <BR>\n" );
document.write( "* **Alternative Hypothesis (H1):** Absenteeism is not evenly distributed throughout the workweek.\r<BR>\n" );
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document.write( "**2. Calculate Expected Frequencies**\r<BR>\n" );
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document.write( "* **Total Absences:** 12 + 9 + 11 + 10 + 9 + 9 = 60 <BR>\n" );
document.write( "* **Expected Absences per Day (under the null hypothesis):** 60 absences / 6 days = 10 absences/day\r<BR>\n" );
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document.write( "* **Create a table:**\r<BR>\n" );
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document.write( "| Day       | Observed (O) | Expected (E) | (O - E)² | (O - E)² / E |<BR>\n" );
document.write( "|-----------|-------------|-------------|---------|-------------|<BR>\n" );
document.write( "| Monday    | 12          | 10          | 4       | 0.4        |<BR>\n" );
document.write( "| Tuesday   | 9           | 10          | 1       | 0.1        |<BR>\n" );
document.write( "| Wednesday | 11          | 10          | 1       | 0.1        |<BR>\n" );
document.write( "| Thursday  | 10          | 10          | 0       | 0          |<BR>\n" );
document.write( "| Friday    | 9           | 10          | 1       | 0.1        |<BR>\n" );
document.write( "| Saturday  | 9           | 10          | 1       | 0.1        |<BR>\n" );
document.write( "| **Total** | 60          | 60          |   | **0.8**      |\r<BR>\n" );
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document.write( "**3. Calculate the Chi-Square Test Statistic**\r<BR>\n" );
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document.write( "* χ² = Σ [(O - E)² / E] = 0.8\r<BR>\n" );
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document.write( "**4. Determine Degrees of Freedom**\r<BR>\n" );
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document.write( "* Degrees of Freedom (df) = Number of categories - 1 = 6 - 1 = 5\r<BR>\n" );
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document.write( "**5. Find the Critical Value**\r<BR>\n" );
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document.write( "* Using a chi-square distribution table, find the critical value for α = 0.01 and df = 5. <BR>\n" );
document.write( "* The critical value is approximately 15.086.\r<BR>\n" );
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document.write( "**6. Make a Decision**\r<BR>\n" );
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document.write( "* **Compare the calculated chi-square statistic to the critical value:**<BR>\n" );
document.write( "    * 0.8 < 15.086\r<BR>\n" );
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document.write( "* **Decision:** Since the calculated chi-square statistic (0.8) is less than the critical value (15.086), we **fail to reject the null hypothesis**.\r<BR>\n" );
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document.write( "**7. Conclusion**\r<BR>\n" );
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document.write( "* There is **not enough evidence** at the 0.01 level of significance to conclude that absenteeism is not evenly distributed throughout the workweek. \r<BR>\n" );
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document.write( "**Interpretation for the Human Resources Director:**\r<BR>\n" );
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document.write( "* This analysis suggests that there is no significant evidence to indicate that absenteeism is more prevalent on any particular day of the week. <BR>\n" );
document.write( "* The observed variations in absenteeism across the days could be due to random chance. <BR>\n" );
document.write( "* The HR director may need to investigate other factors that might be contributing to absenteeism, such as employee health, work-life balance, or job satisfaction.\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This analysis assumes that the data meets the assumptions of the chi-square test, such as expected frequencies being sufficiently large (generally, expected frequencies should be greater than 5).\r<BR>\n" );
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document.write( "This analysis provides a basic framework for conducting a chi-square goodness-of-fit test. <BR>\n" );
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