document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155043>Question 1155043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Nationwide, the average waiting time until a electric utility customer service representative answers a call is 260 seconds.  The Gigantic Kilowatt Energy Company randomly sampled 30 calls and found that, on average, they were answered in 227 seconds with a population standard deviation of 40 seconds.  Can the company claim that they are faster than the average utility at α = 0.05?\r<BR>\n" );
document.write( "\n" );
document.write( "            A)      Yes, because the test value  -  4.52 falls in the critical region.\r<BR>\n" );
document.write( "\n" );
document.write( "            B)      No, because the test value  -  0.83 falls in the critical region.\r<BR>\n" );
document.write( "\n" );
document.write( "            C)      Yes, because the test value  -  0.15 falls in the critical region.\r<BR>\n" );
document.write( "\n" );
document.write( "            D)      No, because the test value  -  0.15 falls in the critical region. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777707 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=777707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "mu = 260 is the population mean<BR>\n" );
document.write( "xbar = 227 is the sample mean<BR>\n" );
document.write( "sigma = 40 is the population standard deviation<BR>\n" );
document.write( "n = 30 is the sample size\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Compute the z score<BR>\n" );
document.write( "z = (xbar - mu)/(sigma/sqrt(n))<BR>\n" );
document.write( "z = (227-260)/(40/sqrt(30))<BR>\n" );
document.write( "z = -4.51871109941762<BR>\n" );
document.write( "z = -4.52<BR>\n" );
document.write( "The test statistic, or test value, is approximately -4.52\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The critical value can be found through <a  rel=nofollow HREF=\"http://www.ttable.org/\">this table</a> (tables such as this can be found in the back of your textbook). According to that table, the solution to P(Z < k) = 0.95 is roughly k = 1.645<BR>\n" );
document.write( "In other words, P(Z < 1.645) = 0.95<BR>\n" );
document.write( "We make this value negative because we are below the mean.<BR>\n" );
document.write( "Therefore, the critical value is approximately -1.645<BR>\n" );
document.write( "meaning that, P(Z < -1.645) = 0.05\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red size=4>A) Yes, because the test value -4.52 falls in the critical region.</font> (the boundary is set at the critical value -1.645)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/TlRWXNL.png\"><BR>\n" );
document.write( "The critical region is another name for the rejection region. <BR>\n" );
document.write( "The null hypothesis is mu = 260, the alternative is mu < 260.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );