document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192382>Question 1192382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an experiment designed to test the effectiveness of paroxetine for treating bipolar<BR>\n" );
document.write( "depression, subjects were measured using the Hamilton Depression Scale with the results given below (based on data from ”Double-Blind, Placebo-Controlled Comparison<BR>\n" );
document.write( "of Imipramine and Paroxetine in the Treatment of Bipolar Depression” by Nemeroff,<BR>\n" );
document.write( "Evans, et al., American Journal of Psychiatry, Vol. 158, No. 6). use a 0.05 significance<BR>\n" );
document.write( "level to test the claim that the treatment group and placebo group come from populations with the same mean. What does the result of the hypothesis test suggest about<BR>\n" );
document.write( "paroxetine as a treatment for bipolar depression? (7 pts)<BR>\n" );
document.write( "Placebo Group n = 43 x¯ = 21.57 s = 3.87<BR>\n" );
document.write( "Paroxetine Treatment Group n = 33 x¯ = 20.38 s = 3.91 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848999 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.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=848999\">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):** The mean Hamilton Depression Scale score for the placebo group is equal to the mean score for the paroxetine treatment group (μ1 = μ2).<BR>\n" );
document.write( "* **Alternative Hypothesis (H1):** The mean Hamilton Depression Scale score for the placebo group is not equal to the mean score for the paroxetine treatment group (μ1 ≠ μ2).\r<BR>\n" );
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document.write( "**2. Perform Independent Samples t-test**\r<BR>\n" );
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document.write( "* We will use an independent samples t-test to compare the means of the two groups. <BR>\n" );
document.write( "* Since the sample standard deviations are similar (3.87 and 3.91), we can assume equal variances for the t-test.\r<BR>\n" );
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document.write( "* **Calculate the t-statistic:**<BR>\n" );
document.write( "    * t = (x̄1 - x̄2) / √[(s1²/n1) + (s2²/n2)] <BR>\n" );
document.write( "        * where:<BR>\n" );
document.write( "            * x̄1 = mean of placebo group <BR>\n" );
document.write( "            * x̄2 = mean of treatment group<BR>\n" );
document.write( "            * s1 = standard deviation of placebo group<BR>\n" );
document.write( "            * s2 = standard deviation of treatment group<BR>\n" );
document.write( "            * n1 = sample size of placebo group<BR>\n" );
document.write( "            * n2 = sample size of treatment group\r<BR>\n" );
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document.write( "    * t = (21.57 - 20.38) / √[(3.87²/43) + (3.91²/33)] <BR>\n" );
document.write( "    * t ≈ 1.323\r<BR>\n" );
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document.write( "* **Determine the degrees of freedom:**<BR>\n" );
document.write( "    * Degrees of freedom (df) = n1 + n2 - 2 = 43 + 33 - 2 = 74\r<BR>\n" );
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document.write( "* **Find the p-value:**<BR>\n" );
document.write( "    * Using a t-distribution table or statistical software, find the p-value associated with the calculated t-statistic (1.323) and 74 degrees of freedom.\r<BR>\n" );
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document.write( "* **Result:** <BR>\n" );
document.write( "    * The p-value is approximately 0.1900.\r<BR>\n" );
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document.write( "**3. Make a Decision**\r<BR>\n" );
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document.write( "* **Significance Level (α):** 0.05\r<BR>\n" );
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document.write( "* **Compare p-value to α:**<BR>\n" );
document.write( "    * Since the p-value (0.1900) is greater than the significance level (0.05), we **fail to reject the null hypothesis**.\r<BR>\n" );
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document.write( "**4. Conclusion**\r<BR>\n" );
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document.write( "* **Based on the results of the t-test, there is not enough evidence to suggest that paroxetine treatment is significantly different from placebo in reducing bipolar depression symptoms.** <BR>\n" );
document.write( "* The observed difference in mean scores between the groups could be due to chance.\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 t-test, such as independent samples and normally distributed data.<BR>\n" );
document.write( "* Further research and larger sample sizes may be needed to draw more definitive conclusions about the effectiveness of paroxetine for treating bipolar depression.\r<BR>\n" );
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document.write( "This analysis provides a framework for interpreting the results of the study. <BR>\n" );
document.write( " </SPAN>\n" );
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