document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=836101>Question 836101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher claims that the average score in the 2012 final exam of ST130 students is at least 69%. A random sample of 10 students is selected, and the scores in percentage are shown.  48     11     84     72     15 52     35     63     61     58 At &#61537; = 0.025, is there enough evidence to reject the claim?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503991 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=503991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A researcher claims that the average score in the 2012 final exam of ST130 students is at least 69%. A random sample of 10 students is selected, and the scores in percentage are shown. 48 11 84 72 15 52 35 63 61 58 At alpha = 0.025, is there enough evidence to reject the claim? <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Ho: p >= 0.69 (claim)<BR>\n" );
document.write( "Ha: p < 0.69<BR>\n" );
document.write( "------<BR>\n" );
document.write( "p-hat = 49.9<BR>\n" );
document.write( "std = 23.5<BR>\n" );
document.write( "------<BR>\n" );
document.write( "z(49.9) = (49.9-69)/[23.5/sqrt(10)] = -2.57<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "p-value = P(z < -2.57) = normalcdf(-100,-2.57) = 0.0051<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Conclusion: Since the p-value is less than 2.5%, reject Ho.<BR>\n" );
document.write( "Reject the claim.<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============== </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );