document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140488>Question 140488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two-Sample T-Test<BR>\n" );
document.write( "We want to know whether the means of two populations on some outcome differ. For example, we want to compare two categories of males and females two populations’ age difference in purchasing concert tickets. The two-sample t-test is a hypothesis test for answering questions about the mean where the data are collected from two random samples of independent observations, each from an underlying normal distribution: <BR>\n" );
document.write( "The steps of conducting a two-sample t-test are quite similar to those of the one-sample test. And for the sake of consistency, we will focus on another example dealing with ages of ticket purchase. <BR>\n" );
document.write( "Returning to the two-sample t-test, the steps to conduct the test are similar to those of the one- sample test. <BR>\n" );
document.write( "Establish hypotheses<BR>\n" );
document.write( "The first step to examining this question is to establish the specific hypotheses we wish to examine. Specifically, we want to establish a null hypothesis and an alternative hypothesis to be evaluated with data. <BR>\n" );
document.write( "In this case: <BR>\n" );
document.write( "•	Null hypothesis is that the difference between the two groups is 0. Another way of stating the null hypothesis is that the difference between the mean of the treatment group of ages for ticket purchasers and the mean of the men and women who purchase tickets is zero. <BR>\n" );
document.write( "Calculate test statistic<BR>\n" );
document.write( "Calculation of the test statistic requires three components: <BR>\n" );
document.write( "1. The average of both sample (observed averages)<BR>\n" );
document.write( "Statistically, we represent these as <BR>\n" );
document.write( " <BR>\n" );
document.write( "2. The standard deviation (SD) of both averages<BR>\n" );
document.write( "Statistically, we represent these as <BR>\n" );
document.write( " <BR>\n" );
document.write( "3. The number of observations in both populations, represented as<BR>\n" );
document.write( " <BR>\n" );
document.write( "From hospital records, we obtain the following values for these components: <BR>\n" );
document.write( " 	men	women<BR>\n" );
document.write( "Average age	29.87	31.67<BR>\n" );
document.write( "SD	8.45	8.10<BR>\n" );
document.write( "n	15	15<BR>\n" );
document.write( "With these pieces of information, we calculate the following statistic, t: <BR>\n" );
document.write( " <BR>\n" );
document.write( "Use this value to determine p-value<BR>\n" );
document.write( "Having calculated the t-statistic, compare the t-value with a standard table of t-values to determine whether the t-statistic reaches the threshold of statistical significance. <BR>\n" );
document.write( "With a t-score -1.80 not significant, the p-value is 0.7218, a score that forms our basis to reject the null hypothesis and conclude that the age data for both male and female who purchase tickets are not 34. \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 #102326 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=102326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Calculation of the test statistic requires three components: <BR>\n" );
document.write( "1. The average of both sample (observed averages)<BR>\n" );
document.write( "Statistically, we represent these as <BR>\n" );
document.write( "Ans: u1 and u2<BR>\n" );
document.write( "--------------------\r<BR>\n" );
document.write( "\n" );
document.write( "2. The standard deviation (SD) of both averages<BR>\n" );
document.write( "Statistically, we represent these as <BR>\n" );
document.write( "s1 and s2<BR>\n" );
document.write( "--------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "3. The number of observations in both populations, represented as<BR>\n" );
document.write( "n1 and n2<BR>\n" );
document.write( "---------------------\r<BR>\n" );
document.write( "\n" );
document.write( "From hospital records, we obtain the following values for these components: <BR>\n" );
document.write( "men women<BR>\n" );
document.write( "Average age 29.87 31.67<BR>\n" );
document.write( "SD 8.45 8.10<BR>\n" );
document.write( "n 15 15<BR>\n" );
document.write( "With these pieces of information, we calculate the following statistic, t: <BR>\n" );
document.write( "t(29.87-31.67) = (-1.8 - 0)/[8.45^2/15 + 8.10^2/15] = -1.8/3.0222 = -0.5956<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Use this value to determine p-value<BR>\n" );
document.write( "p-value = p(-0.5956 < z < 10) = 0.7243...<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "Having calculated the t-statistic, compare the t-value with a standard table of t-values to determine whether the t-statistic reaches the threshold of statistical significance. <BR>\n" );
document.write( "Critical value of one-tail t-test with df = 29 and alpha=5%: t=-1.645<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "With a t-score -1.80 not significant, the p-value is 0.7218, a score that forms our basis to reject the null hypothesis and conclude that the age data for both male and female who purchase tickets are not 34. <BR>\n" );
document.write( "Is this a statement or a question?<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );