document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174400>Question 1174400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain food stall, 278 out of 500 randomly selected consumers indicate their preference for a new kind of food combination. Use a 99% confidence interval to estimate the true proportion p who like the new food combination.<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 #850668 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=850668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. State the Hypotheses:**\r<BR>\n" );
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document.write( "* **Null Hypothesis (H0):** The sample is from a population with a mean height of 171.20 cm (µ = 171.20).<BR>\n" );
document.write( "* **Alternative Hypothesis (H1):** The sample is not from a population with a mean height of 171.20 cm (µ ≠ 171.20).\r<BR>\n" );
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document.write( "**2. Determine the Significance Level:**\r<BR>\n" );
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document.write( "* Alpha (α) = 0.05\r<BR>\n" );
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document.write( "**3. Calculate the Test Statistic:**\r<BR>\n" );
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document.write( "* Since we have a large sample size (n = 400) and know the population standard deviation, we'll use a z-test.<BR>\n" );
document.write( "* z = (sample mean - population mean) / (population standard deviation / √sample size)<BR>\n" );
document.write( "* z = (171.40 - 171.20) / (3.3 / √400) = 0.20 / 0.165 ≈ 1.21\r<BR>\n" );
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document.write( "**4. Determine the Critical Value:**\r<BR>\n" );
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document.write( "* For a two-tailed test at α = 0.05, the critical z-value is ±1.96.\r<BR>\n" );
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document.write( "**5. Compare the Test Statistic to the Critical Value:**\r<BR>\n" );
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document.write( "* Our calculated z-value (1.21) falls within the range of -1.96 to +1.96.\r<BR>\n" );
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document.write( "**6. Make a Decision:**\r<BR>\n" );
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document.write( "* Since the test statistic falls within the acceptance region, we **fail to reject the null hypothesis**.\r<BR>\n" );
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document.write( "**7. Conclusion:**\r<BR>\n" );
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document.write( "* At a 5% level of significance, there is not enough evidence to conclude that the sample of 400 males with a mean height of 171.40 cm is not from a population with a mean height of 171.20 cm and a standard deviation of 3.3. Therefore, **it can be reasonably regarded as a sample from that population.** </SPAN>\n" );
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