document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168856>Question 1168856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a sample of 400 male students is found to have a mean height of 67.47 inches.can it be reasonably regarded as a sample from a large population with mean height 67.39 inches and standard deviation 1.3 inches?test at 5% level of significance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851489 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</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=851489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this hypothesis test step-by-step.\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 sample mean height is equal to the population mean height.<BR>\n" );
document.write( "    * H₀: µ = 67.39 inches<BR>\n" );
document.write( "* **Alternative Hypothesis (H₁):** The sample mean height is not equal to the population mean height.<BR>\n" );
document.write( "    * H₁: µ ≠ 67.39 inches (This is a two-tailed test)\r<BR>\n" );
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document.write( "**2. Set the Significance Level**\r<BR>\n" );
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document.write( "* α = 0.05 (5% significance level)\r<BR>\n" );
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document.write( "**3. Calculate the Test Statistic**\r<BR>\n" );
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document.write( "* Since the population standard deviation is known, we will use a z-test.<BR>\n" );
document.write( "* Given:<BR>\n" );
document.write( "    * Sample mean (x̄) = 67.47 inches<BR>\n" );
document.write( "    * Population mean (µ) = 67.39 inches<BR>\n" );
document.write( "    * Population standard deviation (σ) = 1.3 inches<BR>\n" );
document.write( "    * Sample size (n) = 400<BR>\n" );
document.write( "* Formula for z-statistic:<BR>\n" );
document.write( "    * z = (x̄ - µ) / (σ / √n)<BR>\n" );
document.write( "* Calculation:<BR>\n" );
document.write( "    * z = (67.47 - 67.39) / (1.3 / √400)<BR>\n" );
document.write( "    * z = 0.08 / (1.3 / 20)<BR>\n" );
document.write( "    * z = 0.08 / 0.065<BR>\n" );
document.write( "    * z ≈ 1.23\r<BR>\n" );
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document.write( "**4. Determine the Critical Values**\r<BR>\n" );
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document.write( "* For a two-tailed test at α = 0.05, the critical z-values are ±1.96.\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 z-statistic (1.23) to the critical z-values (±1.96).<BR>\n" );
document.write( "* Since -1.96 < 1.23 < 1.96, the calculated z-statistic falls within the acceptance region.<BR>\n" );
document.write( "* Therefore, we fail to reject the null hypothesis.\r<BR>\n" );
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document.write( "**6. Draw a Conclusion**\r<BR>\n" );
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document.write( "* There is not enough evidence to reject the null hypothesis at the 5% significance level.<BR>\n" );
document.write( "* We cannot reasonably say that the sample mean height is significantly different from the population mean height.<BR>\n" );
document.write( "* In other words, it can be reasonably regarded as a sample from the population.<BR>\n" );
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