document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031434>Question 1031434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average commission charged by a brokerage companies on a sale is $186. However it is seen in the random sample of 133 trades that the average amount of commission paid is $179 with a standard deviation of $61. At 10% significance level can we conclude that the average commission is lower than the industry average?<BR>\n" );
document.write( "	The average commission is not same as $186<BR>\n" );
document.write( "	The average commission is same $186<BR>\n" );
document.write( "	The average commission is lower than $186<BR>\n" );
document.write( "	The average commission is now $179<BR>\n" );
document.write( "Am I correct in assuming that this is an example of T distribution as population standard deviation is not given. Or do we have to you normal distribution.<BR>\n" );
document.write( "Thanks.<BR>\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 #646166 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes, your assumption is correct.<BR>\n" );
document.write( "Ho=same or more<BR>\n" );
document.write( "Ha=less  They are asking whether this is lower than the industry average.  This is a one-way test, not a two way test, which would ask whether it were the same or different.<BR>\n" );
document.write( "alpha=0.10<BR>\n" );
document.write( "critical value about -1.285<BR>\n" );
document.write( "t df=132 = (179-186)/61/sqrt(133)<BR>\n" );
document.write( "t=-7(sqrt(133))/61<BR>\n" );
document.write( "=-1.32<BR>\n" );
document.write( "this is significant, because t<-1.285 , and the average commission is less than $186.<BR>\n" );
document.write( "We use the t-distribution because the sample sd is used as an estimate for the population sd.  The sample size of 30 has been used as a cutoff point for years, for unclear reasons.  If the distribution is near normal, a sample size of greater than 10 would be sufficient to use the normal distribution.  If the distribution is skewed, even a sample size of 100 might not be sufficient.  In any case, the error gets less an less with larger sample sizes, and over 100, the error is about 2%. </SPAN>\n" );
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