document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171312>Question 1171312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A female patient has had her red blood cell count tested on 6 occasions. A mean of 4.4<BR>\n" );
document.write( "with sample standard deviation, s, of 0.28 was found. Generally, healthy, female adults<BR>\n" );
document.write( "have a red blood cell count of 4.8. Conduct a hypothesis test to determine if the red<BR>\n" );
document.write( "blood cell count for this patient is lower than normal. (Use a = 0.05.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796298 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=796298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Hypothesis:<BR>\n" );
document.write( "H0: mu = 4.8<BR>\n" );
document.write( "H1: mu < 4.8<BR>\n" );
document.write( "Left tailed test\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "alpha = 0.05\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 6 is the sample size<BR>\n" );
document.write( "Because n < 30 and sigma is not known, this means we must use a T test. Sigma is the population standard deviation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "While the population standard deviation is not known, the population mean (mu) is known. In this case, it is mu = 4.8, which is how the hypothesis is formed above.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For the female patient, the samples lead to<BR>\n" );
document.write( "xbar = sample mean = 4.4<BR>\n" );
document.write( "s = sample standard deviation = 0.28\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The standard error (SE) is<BR>\n" );
document.write( "SE = s/sqrt(n)<BR>\n" );
document.write( "SE = 0.28/sqrt(6)<BR>\n" );
document.write( "SE = 0.11430952132989\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The T test statistic is<BR>\n" );
document.write( "t = (xbar - mu)/(SE)<BR>\n" );
document.write( "t = (4.4 - 4.8)/(0.11430952132989)<BR>\n" );
document.write( "t = -3.49927106111857<BR>\n" );
document.write( "t = -3.499271\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use a T cdf function on your calculator to find that <BR>\n" );
document.write( "P(T < -3.499271) = 0.0086 approximately when df = n-1 = 5<BR>\n" );
document.write( "df = degrees of freedom<BR>\n" );
document.write( "So the p value is approximately 0.0086<BR>\n" );
document.write( "This p value is smaller than alpha = 0.05, so we reject the null and conclude that mu < 4.8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another way to reject the null is to notice that the test statistic (-3.499271) is to the left of the T critical value (-2.015) when alpha = 0.05 and df = 5. Use a calculator or a T table to find the T critical value. So this test statistic is in the rejection region.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Interpretation: Her mean red blood cell count is less than 4.8, which means it's lower than normal.<BR>\n" );
document.write( "</font>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );