document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207829>Question 1207829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1 Test the claim that the mean body temperature of normal and healthy adults is equal <BR>\n" );
document.write( "to 37°C.  Sample data consist of 20 randomly selected healthy adults who have <BR>\n" );
document.write( "body temperatures with a mean of 36.78° and a standard deviation of 0.35°.  Use a <BR>\n" );
document.write( "0.05 level of significance. <BR>\n" );
document.write( "2. Using the same sample data given in problem 1, test the claim that the standard <BR>\n" );
document.write( "deviation of body temperatures for normal healthy adults is less than 1.00°C.  Use a <BR>\n" );
document.write( "0.05 level of significance. <BR>\n" );
document.write( "3. Use a 0.05 level of significance to test Bill Bradley’s claim that the majority of voters <BR>\n" );
document.write( "would vote for him.  Assume that sample data consist of 1068 randomly selected <BR>\n" );
document.write( "voters, 540 of whom indicated that they would vote for Bradley. <BR>\n" );
document.write( "4. The Sylvan Pharmaceutical Company makes tubes of antibacterial cream that are <BR>\n" );
document.write( "labeled as containing 4 oz.  In testing the claim that the mean content amount is less <BR>\n" );
document.write( "than 4 oz., a P-value of 0.220 is obtained.  What do you conclude? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845953 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=845953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Please ask only one question per post.<BR>\n" );
document.write( "I'll do problem 1 to get you started.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 20 = sample size<BR>\n" );
document.write( "mu = 37 = the claimed population mean body temperature<BR>\n" );
document.write( "xbar = 36.78 = sample mean body temperature<BR>\n" );
document.write( "s = 0.35 = sample standard deviation of the temperatures<BR>\n" );
document.write( "sigma = population standard deviation = unknown<BR>\n" );
document.write( "alpha = level of significance = 0.05\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Null Hypothesis: mu = 37<BR>\n" );
document.write( "Alternative Hypothesis: mu =/= 37<BR>\n" );
document.write( "The claim is made in the null. <BR>\n" );
document.write( "The alternative hypothesis indicates we have a two-tailed test.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We don't know the value of sigma and n > 30 is not the case, so we must use the T distribution.<BR>\n" );
document.write( "df = degrees of freedom<BR>\n" );
document.write( "df = n-1<BR>\n" );
document.write( "df = 20-1<BR>\n" );
document.write( "df = 19\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use a T table such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "Such a table can be found at the back of your stats textbook.<BR>\n" );
document.write( "Highlight the df = 19 row and the column that mentions \"two tails = 0.05\" since this is the alpha level.<BR>\n" );
document.write( "The intersection of this row and column yields the approximate t critical value t = 2.093\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What does this tell us?<BR>\n" );
document.write( "It tells us that P(-2.093 < t < 2.093) = 0.95 approximately when df = 19.<BR>\n" );
document.write( "The 0.95 is the area of the main body while 1-0.95 = 0.05 is the combined area of the two tails. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If the test statistic is in the interval -2.093 < t < 2.093, then we do not reject the null.<BR>\n" );
document.write( "Otherwise, we'll reject the null.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's compute the test statistic.<BR>\n" );
document.write( "testStatistic = (xbar - mu)/( s/sqrt(n) )<BR>\n" );
document.write( "testStatistic = (36.78 - 37)/( 0.35/sqrt(20) )<BR>\n" );
document.write( "testStatistic = -2.811 approximately\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The value t = -2.811 is NOT in the interval -2.093 < t < 2.093<BR>\n" );
document.write( "This value is in the rejection region. It's to the left of the interval mentioned.<BR>\n" );
document.write( "Therefore we'll reject the null and conclude that mu =/= 37 must be the case.<BR>\n" );
document.write( "The claim \"the mean body temperature of normal and healthy adults is equal to 37°C\" appears to be false.<BR>\n" );
document.write( "Either mu > 37 or mu < 37.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another approach using p-value\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We calculated the test statistic to be roughly -2.811<BR>\n" );
document.write( "Let's find the value of P(t < -2.811)<BR>\n" );
document.write( "Use a stats calculator such as a TI83 to determine that P(t < -2.811) = 0.00558 approximately when df = 19.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're doing a two-tailed test, so don't forget to double that result and you would get 2*0.00558 = 0.01116<BR>\n" );
document.write( "This is the approximate p-value.<BR>\n" );
document.write( "It is smaller than alpha (0.05), so we must reject the null. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A useful phrase to remember: \"If the p-value is low, then the null must go\" which would translate to \"if the p-value is smaller than alpha, reject the null\".<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );