document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110954>Question 1110954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of &#956; = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 34 waves showed an average wave height of x = 17.1 feet. Previous studies of severe storms indicate that &#963; = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use &#945; = 0.01.\r<BR>\n" );
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document.write( "(a) What is the level of significance?<BR>\n" );
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document.write( "State the null and alternate hypotheses.<BR>\n" );
document.write( "H0: &#956; = 16.4 ft; H1: &#956; &#8800; 16.4 ft<BR>\n" );
document.write( "H0: &#956; = 16.4 ft; H1: &#956; > 16.4 ft    <BR>\n" );
document.write( "H0: &#956; > 16.4 ft; H1: &#956; = 16.4 ft<BR>\n" );
document.write( "H0: &#956; < 16.4 ft; H1: &#956; = 16.4 ft<BR>\n" );
document.write( "H0: &#956; = 16.4 ft; H1: &#956; < 16.4 ft\r<BR>\n" );
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document.write( "(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.<BR>\n" );
document.write( "The standard normal, since the sample size is large and &#963; is known.<BR>\n" );
document.write( "The Student's t, since the sample size is large and &#963; is unknown.    <BR>\n" );
document.write( "The standard normal, since the sample size is large and &#963; is unknown.<BR>\n" );
document.write( "The Student's t, since the sample size is large and &#963; is known.\r<BR>\n" );
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document.write( "What is the value of the sample test statistic? (Round your answer to two decimal places.)<BR>\n" );
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document.write( "(c) Find the P-value. (Round your answer to four decimal places.)<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 #725969 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) level of significance is 1%<BR>\n" );
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document.write( "The null and alternative hypotheses are H0: &#956; = 16.4 ft; H1: &#956; > 16.4 ft<BR>\n" );
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document.write( "(b)  Use the standard normal, since the sample size is large and &#963; is known<BR>\n" );
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document.write( "Note &#963; is the standard deviation of the population<BR>\n" );
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document.write( "Here n=34, which has a square root of 5.831 so the standard error is 3.5/5.831 = 0.6002. <BR>\n" );
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document.write( "Our test statistic is z = (17.1 - 16.4)/0.6002 = 1.1663<BR>\n" );
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document.write( "Using z-tables the probability associated with 1.1663 is 0.8783, this is our p-value<BR>\n" );
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document.write( "since our p-value is > 0.01, we accept the null hypothesis which is that the storm is not increasing above the severe rating<BR>\n" );
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