document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179167>Question 1179167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean life satisfaction for 142 countries around the world in 2016 (on a scale from 0  -  10) was 5.4. A sample of 46 countries taken in 2018 showed a mean of 5.6 with a standard deviation of 1.1. Is the mean life satisfaction for the 2018 sample significantly higher than the mean life satisfaction in 2016? Conduct the appropriate hypothesis test using α = 0.01.\r<BR>\n" );
document.write( "\n" );
document.write( "What is the standard deviation?<BR>\n" );
document.write( "please show steps!<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 #813777 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813777\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B0%5D%3A+mu+=+5.4 ALIGN=MIDDLE  ALT=\"H%5B0%5D%3A+mu+=+5.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B1%5D%3A+mu+%3E+5.4 ALIGN=MIDDLE  ALT=\"H%5B1%5D%3A+mu+%3E+5.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Significance level <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.01\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Test statistic: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28%28X-bar%29+-+mu%29%2F%28s%2Fsqrt%28n%29%29+=+%285.6+-+5.4%29%2F%281.1%2Fsqrt%2846%29%29=1.23315++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  with 45 d.f.\r<BR>\n" );
document.write( "\n" );
document.write( "==> p-value = 0.112 > 0.01 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, do not reject the null hypothesis, and conclude that the mean life satisfaction for 2018 is not significantly higher than in 2016.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );