document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193668>Question 1193668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A study was to investigate the oral status of a group of patients diagnosed with thalassemia major (TM). One of the outcome measures was the decayed, missing, and filled teeth index (DMFT). In a sample of 18 patients the mean DMFT index value was 11.3 with a standard deviation of 6.3. Is this sufficient evidence to allow us to conclude that the mean DMFT index is greater than 9.0 in a population of similar subjects? Let alpha=5% (show all the steps) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848612 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848612\">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):** μ ≤ 9.0 (The population mean DMFT index is less than or equal to 9.0)<BR>\n" );
document.write( "* **Alternative Hypothesis (H1):** μ > 9.0 (The population mean DMFT index is greater than 9.0)\r<BR>\n" );
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document.write( "**2. Calculate the t-statistic**\r<BR>\n" );
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document.write( "* t = (sample mean - population mean) / (sample standard deviation / √sample size)<BR>\n" );
document.write( "* t = (11.3 - 9.0) / (6.3 / √18) <BR>\n" );
document.write( "* t ≈ 1.549\r<BR>\n" );
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document.write( "**3. Determine Degrees of Freedom**\r<BR>\n" );
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document.write( "* Degrees of Freedom (df) = sample size - 1 = 18 - 1 = 17\r<BR>\n" );
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document.write( "**4. Find the Critical Value**\r<BR>\n" );
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document.write( "* Since this is a one-tailed test (we're only interested in whether the mean is *greater* than 9.0), we'll find the critical t-value for a one-tailed test with α = 0.05 and df = 17. <BR>\n" );
document.write( "* Using a t-distribution table or statistical software, the critical t-value is approximately 1.740.\r<BR>\n" );
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document.write( "**5. Make a Decision**\r<BR>\n" );
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document.write( "* **Compare the calculated t-statistic to the critical t-value:**<BR>\n" );
document.write( "    * 1.549 < 1.740\r<BR>\n" );
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document.write( "* **Decision:** Since the calculated t-statistic (1.549) is less than the critical t-value (1.740), we **fail to reject the null hypothesis.**\r<BR>\n" );
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document.write( "**6. Conclusion**\r<BR>\n" );
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document.write( "* There is **not sufficient evidence** at the 0.05 level of significance to conclude that the mean DMFT index in the population of patients with thalassemia major is greater than 9.0.\r<BR>\n" );
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document.write( "**In summary:**\r<BR>\n" );
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document.write( "Based on the sample data, we cannot confidently conclude that the mean DMFT index for patients with thalassemia major is significantly higher than 9.0. \r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This analysis assumes that the sample of patients is representative of the larger population of patients with thalassemia major.<BR>\n" );
document.write( "* It also assumes that the DMFT index values in the population are normally distributed. <BR>\n" );
document.write( "* If these assumptions are not met, the results of the t-test may not be reliable.<BR>\n" );
document.write( " </SPAN>\n" );
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