document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193195>Question 1193195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My apologies, I did not submit the whole problem. I could really use any assistance. Thank you. I appreciate the help. I believe I should be using a t-score but how when I do not know how to get the population mean. \r<BR>\n" );
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document.write( "A nutrition expert claims that the average American is overweight. To test his claim, a random sample of 26 Americans was selected, and the difference between each person's actual weight and idea weight was calculated. For this data, we have x¯=15.3 and s=27.5. Is there sufficient evidence to conclude that the expert's claim is true? Carry out a hypothesis test at a 2% significance level. Hint: Pay attention to the variable being measured: the difference between actual weight and ideal. A positive value indicates that the person is overweight.\r<BR>\n" );
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document.write( "A. Give the value of the standardized test statistic (give to 3 decimal places): \r<BR>\n" );
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document.write( "B. The p-value is (give to 4 decimal places): <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825223 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=825223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the test statistic is the difference between the person's actual weight and the ideal weight.<BR>\n" );
document.write( "if the difference is positive, the person is overweight.<BR>\n" );
document.write( "if the difference is negative, the person is underweight.<BR>\n" );
document.write( "if the difference is zero, the person is at the ideal weight.<BR>\n" );
document.write( "from the data, it appears the average person is overweight by an average of 15.3 pounds.<BR>\n" );
document.write( "for this test, the population mean is assumed to be the ideal weight = 0.<BR>\n" );
document.write( "sample size = 26<BR>\n" );
document.write( "sample mean = 15.3<BR>\n" );
document.write( "sample standard deviation = 27.5<BR>\n" );
document.write( "population mean is assumed to be 0.<BR>\n" );
document.write( "the standard error is equal to the sample standard deviation divided by the square root of the sample size = 27.5 / sqrt(26) = 5.393194 rounded to 6 decimal places.<BR>\n" );
document.write( "the formula is t = (x - m) / s.<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is he sample mean difference from the ideal.<BR>\n" );
document.write( "m is the assumed population difference from the ideal.<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "it becomes:<BR>\n" );
document.write( "t = (15.3 - 0) / 5.393194 = 2.836909 rounded to 6 decimal places.<BR>\n" );
document.write( "the degrees of freedom = sample size minus 1 = 25.<BR>\n" );
document.write( "area to the right of a t-score of 2.836909 with 25 degrees of freedom = .00451rounded to 6 decimal places.<BR>\n" );
document.write( "area to the right of that t-score = .004451 rounded to 6 decimal places.<BR>\n" );
document.write( "critical t-score with 25 degrees of freedom at 2% one-tail significance level equals 2.166587 rounded to 6 decimal places.<BR>\n" );
document.write( "the critical t-score is less than the sample t-score, indicating the assumption that the average american is overweight is accepted.<BR>\n" );
document.write( "this is also supported by the p-score because the test p-score = .004451 and the critical p-score = .02.<BR>\n" );
document.write( "the test p-score is less than the critical p-score, indicating the results are significant as the .02 significance level.<BR>\n" );
document.write( "here's what it looks like on a graph.<BR>\n" );
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