document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193449>Question 1193449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A paired difference experiment produced the following results:<BR>\n" );
document.write( "nD=49, x1= 176, x2= 183, xD=−7, sD=58,\r<BR>\n" );
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document.write( "(a) Determine the rejection region for the hypothesis H0:μD=0 if Ha:μD>0. Use α=0.03<BR>\n" );
document.write( "- t> ____. (5 sig. figs)\r<BR>\n" );
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document.write( "(b) Conduct a paired difference test described above.\r<BR>\n" );
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document.write( "- The test statistic is ______. (5 sig. figs)<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 #848665 by </B><A HREF=/tutors/aboutme.mpl?userid=yurtman><B>yurtman(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=yurtman><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=848665\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Determine the Rejection Region**\r<BR>\n" );
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document.write( "* **Hypotheses:**<BR>\n" );
document.write( "    * H0: μD = 0 (Null Hypothesis: Mean difference is zero)<BR>\n" );
document.write( "    * Ha: μD > 0 (Alternative Hypothesis: Mean difference is greater than zero) \r<BR>\n" );
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document.write( "* **Significance Level (α):** 0.03\r<BR>\n" );
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document.write( "* **Degrees of Freedom (df):** nD - 1 = 49 - 1 = 48\r<BR>\n" );
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document.write( "* **Find the Critical Value (t-critical) using a t-distribution table or statistical software:**<BR>\n" );
document.write( "    * For a one-tailed test with α = 0.03 and df = 48, t-critical ≈ 1.8856 \r<BR>\n" );
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document.write( "* **Rejection Region:** <BR>\n" );
document.write( "    * t > 1.8856\r<BR>\n" );
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document.write( "**b) Conduct the Paired Difference Test**\r<BR>\n" );
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document.write( "* **Calculate the Test Statistic (t-statistic):**<BR>\n" );
document.write( "    * t = (xD - μD) / (sD / √nD) <BR>\n" );
document.write( "    * t = (-7 - 0) / (58 / √49) <BR>\n" );
document.write( "    * t = -7 / (58 / 7) <BR>\n" );
document.write( "    * t = -0.85087\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **Rejection Region:** t > 1.8856<BR>\n" );
document.write( "* **Test Statistic:** t = -0.85087\r<BR>\n" );
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document.write( "**Conclusion:**\r<BR>\n" );
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document.write( "Since the calculated t-statistic (-0.85087) does not fall within the rejection region (t > 1.8856), we **fail to reject the null hypothesis (H0)**. \r<BR>\n" );
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document.write( "There is **not enough evidence** to conclude that the mean difference (μD) is significantly greater than zero at the 0.03 significance level.<BR>\n" );
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