document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061709>Question 1061709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A class survey in a large class for first-year college students asked, \"About how many hours do you study during a typical week?\" The mean response of the 492 students was <BR>\n" );
document.write( "x = 15.3 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation <BR>\n" );
document.write( "&#963; = 8.5 hours in the population of all first-year students at this university. \r<BR>\n" );
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document.write( "Regard these students as an SRS from the population of all first-year students at this university. Does the study give good evidence that students claim to study more than 15 hours per week on the average?<BR>\n" );
document.write( "(1) State null and alternative hypotheses in terms of the mean study time in hours for the population. <BR>\n" );
document.write( "a) H0: &#956; = 15 hours<BR>\n" );
document.write( "b) Ha: &#956; > 15 hours<BR>\n" );
document.write( "c) H0: &#956; = 15 hours<BR>\n" );
document.write( "d) Ha: &#956; &#8800; 15 hours    <BR>\n" );
document.write( "e) H0: &#956; = 15 hours<BR>\n" );
document.write( "f) Ha: &#956; < 15 hours<BR>\n" );
document.write( "g) H0: &#956; = 15 hours<BR>\n" );
document.write( "h) Ha: &#956; = 15 hours\r<BR>\n" );
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document.write( "(2) What is the value of the test statistic z? (Give your answer to two decimal places.) <BR>\n" );
document.write( "z =  _____<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "(3) What is the P-value of the test? <BR>\n" );
document.write( "a) less than 0.001<BR>\n" );
document.write( "b) between 0.001 and 0.01    <BR>\n" );
document.write( "c) between 0.01 and 0.025<BR>\n" );
document.write( "d) between 0.025 and 0.05<BR>\n" );
document.write( "e) larger than 0.05\r<BR>\n" );
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document.write( "Can you conclude that students do claim to study more than 15 hours per week on average? <BR>\n" );
document.write( "a) Yes, there is sufficient evidence that the average amount of time students claim to study is more than 15 hours per week.<BR>\n" );
document.write( "b) No, there is little evidence that the average amount of time students claim to study is more than 15 hours per week.    <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676487 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't like any of the first choices.  This is a one-sided hypothesis test, whether the students study more than 15 hours.<BR>\n" );
document.write( "it should be<BR>\n" );
document.write( "Ho: mu <=15 hours <BR>\n" );
document.write( "Ha: mu >15 hours.<BR>\n" );
document.write( "A/B are not bad, but both hypotheses must together cover all situations.<BR>\n" );
document.write( "C/D is best, but that tests for a change, not a unidirectional one.<BR>\n" );
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document.write( "The test statistic is z= (x bar-mean)/s/sqrt (n)<BR>\n" );
document.write( "This is 0.3/8.5/sqrt (492)=0.3* sqrt(492)/8.5=0.78=z<BR>\n" );
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document.write( "The p-value is >0.05<BR>\n" );
document.write( "NO, There is insufficient evidence to say that the average amount of time is >15 hours/wk. </SPAN>\n" );
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