document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078507>Question 1078507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> nEED HELP WITH LOWER, UPPER AND P VALUE<BR>\n" );
document.write( "Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let &#945; be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean.<BR>\n" );
document.write( "For a two-tailed hypothesis test with level of significance &#945; and null hypothesis H0: &#956; = k, we reject H0 whenever k falls outside the c = 1 &#8722; &#945; confidence interval for &#956; based on the sample data. When k falls within the c = 1 &#8722; &#945; confidence interval, we do not reject H0.<BR>\n" );
document.write( "(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, &#956;1 &#8722; &#956;2, or p1 &#8722; p2, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the c = 1 &#8722; &#945; confidence interval for the parameter, we reject H0. For example, consider a two-tailed hypothesis test with &#945; = 0.01 and<BR>\n" );
document.write( "H0: &#956; = 20        H1: &#956; &#8800; 20<BR>\n" );
document.write( "A random sample of size 39 has a sample mean x = 23 from a population with standard deviation &#963; = 5.<BR>\n" );
document.write( "(a) What is the value of c = 1 &#8722; &#945;? <BR>\n" );
document.write( " <BR>\n" );
document.write( ".99<BR>\n" );
document.write( " <BR>\n" );
document.write( "Correct: Your answer is correct.<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "Construct a 1 &#8722; &#945; confidence interval for &#956; from the sample data. (Round your answers to two decimal places.) <BR>\n" );
document.write( "lower limit    	 <BR>\n" );
document.write( "17.57<BR>\n" );
document.write( " <BR>\n" );
document.write( "Incorrect: Your answer is incorrect.<BR>\n" );
document.write( "upper limit    	 <BR>\n" );
document.write( "25.17<BR>\n" );
document.write( " <BR>\n" );
document.write( "Incorrect: Your answer is incorrect.\r<BR>\n" );
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document.write( "What is the value of &#956; given in the null hypothesis (i.e., what is k)? <BR>\n" );
document.write( "k =  <BR>\n" );
document.write( "20<BR>\n" );
document.write( " <BR>\n" );
document.write( "Correct: Your answer is correct.<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "Is this value in the confidence interval? <BR>\n" );
document.write( "Yes<BR>\n" );
document.write( "No    <BR>\n" );
document.write( "Correct: Your answer is correct.\r<BR>\n" );
document.write( "\n" );
document.write( "Do we reject or fail to reject H0 based on this information?<BR>\n" );
document.write( "We fail to reject the null hypothesis since &#956; = 20 is not contained in this interval.<BR>\n" );
document.write( "We fail to reject the null hypothesis since &#956; = 20 is contained in this interval.    <BR>\n" );
document.write( "We reject the null hypothesis since &#956; = 20 is not contained in this interval.<BR>\n" );
document.write( "We reject the null hypothesis since &#956; = 20 is contained in this interval.<BR>\n" );
document.write( "Correct: Your answer is correct.\r<BR>\n" );
document.write( "\n" );
document.write( "(b) Using methods of this chapter, find the P-value for the hypothesis test. (Round your answer to four decimal places.) <BR>\n" );
document.write( " <BR>\n" );
document.write( ".0034<BR>\n" );
document.write( " <BR>\n" );
document.write( "Incorrect: Your answer is incorrect.<BR>\n" );
document.write( " <BR>\n" );
document.write( "thANK YOU! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693011 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=693011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The 99% CI is mean +/- z(0.995) sigma/sqrt(39)<BR>\n" );
document.write( "(20.94, 25.06)<BR>\n" );
document.write( "This is 2.576*5/sqrt(39)=2.06<BR>\n" );
document.write( "20 is not in the CI<BR>\n" );
document.write( "p-value will be very small.<BR>\n" );
document.write( "It is <0.0002<BR>\n" );
document.write( "Note: if the CI doesn't contain what is hypothesized, the p-value is less than alpha.<BR>\n" );
document.write( "If the p-value is less than alpha, the CI won't contain the CI.  That is a basic check to do. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );