document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076818>Question 1076818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stuck on p value.  Thanks for help!<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; = 6.<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" );
document.write( "\n" );
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( "20.53<BR>\n" );
document.write( " <BR>\n" );
document.write( "Correct: Your answer is correct.<BR>\n" );
document.write( "upper limit    	 <BR>\n" );
document.write( "25.47<BR>\n" );
document.write( " <BR>\n" );
document.write( "Correct: Your answer is correct.\r<BR>\n" );
document.write( "\n" );
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" );
document.write( "\n" );
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( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691429 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=691429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the z-value for mean of 23<BR>\n" );
document.write( "z=(23-20)/6/sqrt (39)=3*sqrt(39)/6=3.1224<BR>\n" );
document.write( "p-value is 0.0018<BR>\n" );
document.write( "I found the upper interval probability, which is .0009.  I need to double that to get the lower interval probability as well, which is 0.0018 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );