document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171743>Question 1171743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hinton Press hypothesizes that the average life of its largest web press is 14,500 hours.  They know that the standard deviation of press life is 2,100 hours.  From  a sample of 25 presses, the company finds a sample mean of 13,000 hours.  At a 0.01 significance level, should the company conclude that the average life of the presses is less than the hypothesized 14,500 hours? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850875 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.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=850875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this hypothesis testing problem:\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 average life of the web presses is 14,500 hours (μ = 14,500).<BR>\n" );
document.write( "* **Alternative Hypothesis (H₁):** The average life of the web presses is less than 14,500 hours (μ < 14,500). This is a left-tailed test.\r<BR>\n" );
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document.write( "**2. Gather the Given Information:**\r<BR>\n" );
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document.write( "* Hypothesized mean (μ₀): 14,500 hours<BR>\n" );
document.write( "* Population standard deviation (σ): 2,100 hours<BR>\n" );
document.write( "* Sample mean (x̄): 13,000 hours<BR>\n" );
document.write( "* Sample size (n): 25<BR>\n" );
document.write( "* Significance level (α): 0.01\r<BR>\n" );
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document.write( "**3. Calculate the Test Statistic (z-score):**\r<BR>\n" );
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document.write( "Since we know the population standard deviation, we'll use a z-test.\r<BR>\n" );
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document.write( "z = (x̄ - μ₀) / (σ / √n)\r<BR>\n" );
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document.write( "z = (13,000 - 14,500) / (2,100 / √25)<BR>\n" );
document.write( "z = -1,500 / (2,100 / 5)<BR>\n" );
document.write( "z = -1,500 / 420<BR>\n" );
document.write( "z ≈ -3.57\r<BR>\n" );
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document.write( "**4. Determine the P-value:**\r<BR>\n" );
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document.write( "* We have a left-tailed test, so we need to find the probability of getting a z-score of -3.57 or less.<BR>\n" );
document.write( "* Using a z-table or calculator, the p-value is approximately 0.0002.\r<BR>\n" );
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document.write( "**5. Compare the P-value to the Significance Level:**\r<BR>\n" );
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document.write( "* p-value (0.0002) < α (0.01)\r<BR>\n" );
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document.write( "**6. Make a Decision:**\r<BR>\n" );
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document.write( "* Since the p-value is less than the significance level, we reject the null hypothesis.\r<BR>\n" );
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document.write( "**7. Conclusion:**\r<BR>\n" );
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document.write( "* There is sufficient evidence to conclude that the average life of the web presses is less than 14,500 hours at a 0.01 significance level.<BR>\n" );
document.write( " </SPAN>\n" );
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