document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193825>Question 1193825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Two-Way ANOVA Summary Table is shown below.<BR>\n" );
document.write( "Source SS  d.f.  MS  F<BR>\n" );
document.write( "Factor A 16.63 2 8.31 4.89<BR>\n" );
document.write( "Factor B 5.13 2 2.57 1.51<BR>\n" );
document.write( "Interaction A × B 17.88 4 4.47 2.63<BR>\n" );
document.write( "Within (error) 61.20 36 1.7<BR>\n" );
document.write( "  Total 100.844 44<BR>\n" );
document.write( " The critical value for the F test using = 0.05, d.f.N. = 2, and d.f.D = 36 is 3.26. Then,<BR>\n" );
document.write( "A.only the null hypothesis concerning Factor A should be rejected.<BR>\n" );
document.write( "B.only the null hypothesis concerning Factor B should be rejected.<BR>\n" );
document.write( "C.all of the null hypotheses should be accepted. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848564 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=848564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To answer this question, we compare the **F values** for each factor and interaction term to the critical value (\( F_{critical} = 3.26 \)) provided for \( \alpha = 0.05 \), \( \text{d.f.}_{\text{numerator}} = 2 \), and \( \text{d.f.}_{\text{denominator}} = 36 \).\r<BR>\n" );
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document.write( "### Step 1: Analyze \( F \)-statistics\r<BR>\n" );
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document.write( "1. **Factor A**:<BR>\n" );
document.write( "   - \( F_A = 4.89 \)<BR>\n" );
document.write( "   - \( F_A > 3.26 \): **Reject the null hypothesis** for Factor A.\r<BR>\n" );
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document.write( "2. **Factor B**:<BR>\n" );
document.write( "   - \( F_B = 1.51 \)<BR>\n" );
document.write( "   - \( F_B < 3.26 \): **Do not reject the null hypothesis** for Factor B.\r<BR>\n" );
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document.write( "3. **Interaction A × B**:<BR>\n" );
document.write( "   - \( F_{A \times B} = 2.63 \)<BR>\n" );
document.write( "   - \( F_{A \times B} < 3.26 \): **Do not reject the null hypothesis** for the interaction term.\r<BR>\n" );
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document.write( "### Step 2: Conclusion\r<BR>\n" );
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document.write( "- The null hypothesis for **Factor A** is rejected because its \( F \)-statistic is greater than the critical value.<BR>\n" );
document.write( "- The null hypotheses for **Factor B** and the **interaction term** are not rejected because their \( F \)-statistics are less than the critical value.\r<BR>\n" );
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document.write( "### Final Answer:  <BR>\n" );
document.write( "**A. Only the null hypothesis concerning Factor A should be rejected.** </SPAN>\n" );
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