document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395264>Question 395264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you are performing a one sample hypothesis test of the mean and the standard deviation of the population is unknown, do you use a t-test or a z-test?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280520 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=280520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the appropriate test \"always\" when the population variance is unknown is to use a t-test.  although as the samples sizes get larger and larger, the t-test and Z-test will converge but this does not happen (based on my experience) until the sample size is greater than 100.<BR>\n" );
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document.write( "The other wrinkle is that if the sample size is small, and the population variance is unknown, you  can only use the t-test if the sample comes from a normal distribution as the central limit theorem can't help you with small samples. </SPAN>\n" );
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