document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170230>Question 1170230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.	Among 10,000 school children, 500 of them are randomly selected for a survey on nutritional status among school age children. Of these 500 school children, 91 are found to be moderately and severely underweight children. At 5% level of significance, is their evidence that the proportion of moderately and severely underweight children is 20%?\r<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 #851237 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=851237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We've already solved this problem in a previous response. Let's recap the steps and the answer.\r<BR>\n" );
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document.write( "**1. Define the Hypotheses**\r<BR>\n" );
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document.write( "* **Null Hypothesis (H0):** The proportion of moderately and severely underweight children is 20% (p = 0.20).<BR>\n" );
document.write( "* **Alternative Hypothesis (H1):** The proportion of moderately and severely underweight children is not 20% (p ≠ 0.20).\r<BR>\n" );
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document.write( "**2. Set the Significance Level**\r<BR>\n" );
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document.write( "* Significance level (α) = 0.05\r<BR>\n" );
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document.write( "**3. Calculate the Sample Proportion**\r<BR>\n" );
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document.write( "* Sample size (n) = 500<BR>\n" );
document.write( "* Number of underweight children in the sample (x) = 91<BR>\n" );
document.write( "* Sample proportion (p̂) = x / n = 91 / 500 = 0.182\r<BR>\n" );
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document.write( "**4. Calculate the Test Statistic (z-score)**\r<BR>\n" );
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document.write( "* Standard error (SE) = √[p(1-p) / n] = √[0.20(0.80) / 500] = √(0.16 / 500) = √0.00032 = 0.0178885<BR>\n" );
document.write( "* z = (p̂ - p) / SE = (0.182 - 0.20) / 0.0178885 = -0.018 / 0.0178885 ≈ -1.006\r<BR>\n" );
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document.write( "**5. Determine the Critical Value**\r<BR>\n" );
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document.write( "* Since this is a two-tailed test (p ≠ 0.20) and α = 0.05, the critical z-values are approximately ±1.96.\r<BR>\n" );
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document.write( "**6. Make a Decision**\r<BR>\n" );
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document.write( "* The calculated z-score (-1.006) falls within the non-rejection region (-1.96 < -1.006 < 1.96).<BR>\n" );
document.write( "* Therefore, we fail to reject the null hypothesis.\r<BR>\n" );
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document.write( "**7. Draw a Conclusion**\r<BR>\n" );
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document.write( "* There is not enough evidence at the 5% significance level to conclude that the proportion of moderately and severely underweight children is different from 20%.\r<BR>\n" );
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document.write( "**Answer**\r<BR>\n" );
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document.write( "No, there is not sufficient evidence to say that the proportion of moderately and severely underweight children is different from 20% at the 5% level of significance.<BR>\n" );
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