document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071969>Question 1071969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount. Each individual volume is not exact, but a volume of iced tea beverages is supposed to average to 300 mL with a standard deviation of 3 mL. The consumer protection group sampled 20 beverages and found the average to be 298.4 mL. Which of the following is the most restrictive level of significance on a hypothesis test that would indicate the company is packaging less than the required average 300 mL?<BR>\n" );
document.write( "1%<BR>\n" );
document.write( "2.5%<BR>\n" );
document.write( "5%.<BR>\n" );
document.write( "10% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686869 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=686869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe 1% would do it.<BR>\n" );
document.write( "that would give you a critical z-factor of plus or minus 2.327.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the z-factor of your sample would be calculated as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sample size = 20<BR>\n" );
document.write( "mean = 298.4<BR>\n" );
document.write( "population standard deviation = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = standard deviation of the population / square root of the sample size.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be equal to 3/sqrt(20).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score = (sample mean minus standard mean) / (3/sqrt(20).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be equal to (298.4 - 300) / (3/sqrt(20) which would be equal to -2.385.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the z-score calculator i used can be found at:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first picture is calculating the critical z-score from an alpha of .01 on the low side of the distribution curve.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that less than 1% of the z-scores will be below this critical z-score.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the second picture is calculating the alpha for the z-score of the sample.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the samle z-score is below the critical z-score at an alpha of 1% which indicates the results of the test are statistically significant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the alpha of the sample is less than the alpha of the critical z-score which tells you the same thing.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sample would have failed all of the alphas shown, but 1% is the most restrictive alpha that it would have failed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/030801.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/030802.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );