document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181239>Question 181239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
document.write( "\n" );
document.write( "can you please explain the steps (formulas) \"in detail\" of finding the p-value uaing a z-test, and a one tailed test and a two tailed test.\r<BR>\n" );
document.write( "\n" );
document.write( "Ex: z= 1764 -1750/ 70/ sqrt 150 = 2.4494 ~ 2.449\r<BR>\n" );
document.write( "\n" );
document.write( "Also how do you find a critical value, do you follow the same steps?\r<BR>\n" );
document.write( "\n" );
document.write( "I have this example but I don't understand where 0.937 came from or what the P is and why there are the <= symbols when doing addition?:\r<BR>\n" );
document.write( "\n" );
document.write( "=P(Z<= -1.531) + P(Z>= 1.531)<BR>\n" );
document.write( "=P (Z<= -1.531)+ (1-P(Z< 1.531))<BR>\n" );
document.write( "=0.063 + (1-0,937)<BR>\n" );
document.write( "=0.126\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you\r<BR>\n" );
document.write( "\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 #135908 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=135908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> can you please explain the steps (formulas) \"in detail\" of finding the p-value uaing a z-test, and a one tailed test and a two tailed test.<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Formula for test statistic: z((x-bar)-u) = ((x-bar)-u)/sqrt[s/sqrt(n)} <BR>\n" );
document.write( "Ex: z= (1764 -1750)/[ 70/ sqrt 150] = 2.4494 ~ 2.449 <BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "If this is a 2-tail test p-value = 2*P(z>2.449) = 2*0.00716 = 0.1433..<BR>\n" );
document.write( "If this is a right-tail test p-value = P(z>2.449) = 0.00716<BR>\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "Comment: This p-value business is an alternative to comparing the <BR>\n" );
document.write( "position of the test statistic to the position of the critical value.<BR>\n" );
document.write( "If the test statistic is not in the rejection interval the p-value<BR>\n" );
document.write( "will be greater than alpha; If the test statistic is in the rejection<BR>\n" );
document.write( "interval the p-value will be less than alpha.<BR>\n" );
document.write( "You can see this if you draw a normal curve, select a z=critical value<BR>\n" );
document.write( "like 1.645 then, arbitrarily place a test-statistic value in the <BR>\n" );
document.write( "critical interval or outside the critical interval.  For a right tail<BR>\n" );
document.write( "test the area to the right of the critical value is alpha,  If the <BR>\n" );
document.write( "test-statistic is in the reject interval the area to the right of the<BR>\n" );
document.write( "test-statistic will be less than alpha.  That area to the right of <BR>\n" );
document.write( "the test-statistic is the P-value.  So if you know the p-value is less<BR>\n" );
document.write( "than alpha you automatically know the test statistic is in the reject<BR>\n" );
document.write( "interval and you Reject Ho.<BR>\n" );
document.write( "------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Also how do you find a critical value, do you follow the same steps?<BR>\n" );
document.write( "A two-tail test with alpha = 5% results in critical values of +1.96<BR>\n" );
document.write( "and -1.96.  (1/2)of alpha is to the right of 1.96 and (1/2) of alpha<BR>\n" );
document.write( "is to the left of -1.96.  You need a calculator or a z-table to determine<BR>\n" );
document.write( "these critical values.<BR>\n" );
document.write( "----------------------------------- <BR>\n" );
document.write( "I have this example but I don't understand where 0.937 came from or what the P is and why there are the <= symbols when doing addition?: <BR>\n" );
document.write( "=P(Z<= -1.531) + P(Z>= 1.531)<BR>\n" );
document.write( "=P (Z<= -1.531)+ (1-P(Z< 1.531))<BR>\n" );
document.write( "=0.063 + (1-0,937)<BR>\n" );
document.write( "=0.126 <BR>\n" );
document.write( "---------<BR>\n" );
document.write( "I looks like you are determining the p-value for a two-tail test.<BR>\n" );
document.write( "The test statistic turned out to be 1.531<BR>\n" );
document.write( "The p-value is P(z<=-1.531) + P(z>=1.531)<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "Note: This is the same as 2*P(z>1.531) because the area to the right<BR>\n" );
document.write( "of z=1.531 is the same as the area to the left of z=-1.531.<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "The area to the left is 0.063.<BR>\n" );
document.write( "The area to the right is 1-the area above z=1.531 which is also 0.063.<BR>\n" );
document.write( "Adding the two you get 2(0.063) = 0.126<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );