document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198922>Question 1198922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis<BR>\n" );
document.write( "of these data, we may conclude that the mean systolic blood pressure for a population of African-American is greater than 140.<BR>\n" );
document.write( "What is the null and alternative hypothesis? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832601 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> test mean = 140<BR>\n" );
document.write( "sample size is 157<BR>\n" );
document.write( "sample mean is 146 with standard deviation of 27<BR>\n" );
document.write( "standard error = standard deviation / square root of sample size = 27 / sqrt(157) = 2.1548 rounded to 4 decimal places. <BR>\n" );
document.write( "t = (x - m) / s = (146 - 140) / 2.1548 = 2.78448 rounded to 5 decimal places<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the test mean<BR>\n" );
document.write( "s is the standard error<BR>\n" );
document.write( "area to the right of that t-score with 156 degrees of freedom = .00301 rounded to 5 decimal places.<BR>\n" );
document.write( "that's the test alpha.<BR>\n" );
document.write( "at 99% one tail on the right confidence interval, the critical alpha is .01.<BR>\n" );
document.write( "since the test alpha of .003 is less than that, you can conclude that the mean systolic blood pressure for a population of african americans is greater than 140.<BR>\n" );
document.write( "the null hypothesis stated that the mean systolic blood pressure for african  americans is not greater than 140.<BR>\n" );
document.write( "the alternative hypothesis states that the mean systolic blood pressure for african americans is greater than 140.<BR>\n" );
document.write( "since the test alpha was less than the critical alpha, the results of the test were considered significant and the null hypothesis was rejected in favor of the alternate hypothesis.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );