document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=925594>Question 925594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 90% confidence interval for the difference between the means of two independent populations with unknown population standard deviations is found to be (-0.2, 5.4).<BR>\n" );
document.write( "Which of the following statements is/are correct? CHECK ALL THAT APPLY. \r<BR>\n" );
document.write( "\n" );
document.write( " A. The standard error of the difference between the two observed sample means is 2.6. <BR>\n" );
document.write( " B. A two-sided two-sample t-test testing for a difference between the two population means is rejected at the 10% significance level. <BR>\n" );
document.write( " C. A two-sided paired t-test testing for a difference between the two population means is rejected at the 10% significance level. <BR>\n" );
document.write( " D. A two-sided two-sample t-test testing for a difference between the two population means is not rejected at the 10% significance level. <BR>\n" );
document.write( " E. A two-sided paired t-test testing for a difference between the two population means is not rejected at the 10% significance level. <BR>\n" );
document.write( " F. None of the above. \r<BR>\n" );
document.write( "\n" );
document.write( "So I am slightly confused with this problem. I know that to conduct a t-test, population means and s.d. are unknown (which they are in this problem?). And since they hinted it at being independent, it cannot be a paired test. \r<BR>\n" );
document.write( "\n" );
document.write( "So I rule out C and E. \r<BR>\n" );
document.write( "\n" );
document.write( "But when I look at A), I wonder, can I even find SE (standard error?). I am not quite sure how...as well as how I can compute the p-value to test whether the results are statistically significant?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561661 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=561661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rule out C and E  and A for sure(we can determine ME not SE) <BR>\n" );
document.write( "90% confidence interval is found to be : (-0.2, 5.4).  <BR>\n" );
document.write( "ME = (5.4-(-.2))/2 = 2.8  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285.4+-+2.8%29+=+2.6 ALIGN=MIDDLE  ALT=\"%285.4+-+2.8%29+=+2.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "90%CI: is 2.6 ± 2.8<BR>\n" );
document.write( "..........<BR>\n" );
document.write( "90% confidence interval is found to be:  2.6 ± 2.8<BR>\n" );
document.write( "...<BR>\n" );
document.write( "unknown population standard deviations... <BR>\n" );
document.write( "the critical value used to determine CI would have been as a <u>t-score</u> rather than a z score<BR>\n" );
document.write( "two-sided: t-value with a  cumulative probability equal to 0.95<BR>\n" );
document.write( "......<BR>\n" );
document.write( "90% confidence interval <u>is found to be</u>:  2.6 ± 2.8   (rules out B)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );