document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186172>Question 1186172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let μ denote the true average reflectometer reading for a new type of paint under consideration. A test of H_0: μ = 20 vs. H_A: μ > 20 will be based on a random sample of size n from a normal population distribution.\r<BR>\n" );
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document.write( "​a. Suppose z=3.3. Calculate the p-value for the hypotheses listed above. Round your answer to four decimal places.\r<BR>\n" );
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document.write( "b. Suppose z=1.6. Calculate the p-value for the hypotheses listed above. Round your answer to four decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849473 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=849473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the p-values for the given hypothesis test:\r<BR>\n" );
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document.write( "**Understanding the Problem**\r<BR>\n" );
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document.write( "We are conducting a one-tailed (right-tailed) z-test.  Our null hypothesis is that the average reflectometer reading is equal to 20 (μ = 20), and our alternative hypothesis is that it is greater than 20 (μ > 20).  The p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated (in this case, a z-score), *assuming the null hypothesis is true*.\r<BR>\n" );
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document.write( "**a. z = 3.3**\r<BR>\n" );
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document.write( "1.  **Find the area to the right of z:** Since this is a right-tailed test, the p-value is the area under the standard normal curve to the *right* of the calculated z-score.\r<BR>\n" );
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document.write( "2.  **Use a z-table or calculator:** Look up the area corresponding to z = 3.3. Most z-tables give the area to the *left*. If that's the case, subtract the value you find from 1 to get the area to the right.\r<BR>\n" );
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document.write( "P(z > 3.3) ≈ 0.0005\r<BR>\n" );
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document.write( "**b. z = 1.6**\r<BR>\n" );
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document.write( "1.  **Find the area to the right of z:** Again, since it is a right-tailed test, the p-value is the area to the right of the given z-score.\r<BR>\n" );
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document.write( "2.  **Use a z-table or calculator:** Look up the area corresponding to z = 1.6.\r<BR>\n" );
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document.write( "P(z > 1.6) ≈ 0.0548\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "*   a. p-value ≈ 0.0005<BR>\n" );
document.write( "*   b. p-value ≈ 0.0548<BR>\n" );
document.write( " </SPAN>\n" );
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