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( "Part A\r<BR>\n" );
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document.write( "Hypothesis:<BR>\n" );
document.write( "H0: mu = 0<BR>\n" );
document.write( "H1: mu > 0<BR>\n" );
document.write( "The mu refers to the population mean of the differences in weight (actual - ideal)\r<BR>\n" );
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document.write( "The claim is that mu > 0 to indicate the average American is overweight. In other words, the claim is that the actual weight exceeds the ideal weight on average.<BR>\n" );
document.write( "The inequality sign in the alternative hypothesis tells us we're doing a right-tailed test.\r<BR>\n" );
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document.write( "As with any hypothesis test, we are testing the null. If the p-value is smaller than alpha, then we reject the null. Otherwise, we fail to reject it.<BR>\n" );
document.write( "Determining the p-value requires the test statistic.\r<BR>\n" );
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document.write( "First let's visit the given info<BR>\n" );
document.write( "n = 26 = sample size<BR>\n" );
document.write( "xbar = 15.3 = sample mean<BR>\n" );
document.write( "s = 27.5 = sample standard deviation<BR>\n" );
document.write( "alpha = 0.02 = 2% significance level\r<BR>\n" );
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document.write( "Now to compute the test statistic.<BR>\n" );
document.write( "t = (xbar - mu)/( s/sqrt(n) )<BR>\n" );
document.write( "t = (15.3 - 0)/( 27.5/sqrt(26) )<BR>\n" );
document.write( "t = 2.83690903847162 approximately<BR>\n" );
document.write( "t = 2.837\r<BR>\n" );
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document.write( "Answer: 2.837\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "I recommend a calculator for this. <BR>\n" );
document.write( "You can use a TI (texas instrument) calculator if you have one handy.\r<BR>\n" );
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document.write( "If you have a TI calculator, then refer to this documentation page<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://tibasicdev.wikidot.com/tcdf\">http://tibasicdev.wikidot.com/tcdf</a><BR>\n" );
document.write( "The tcdf function will give the area under the T curve. The format is<BR>\n" );
document.write( "tcdf(lower, upper, v)<BR>\n" );
document.write( "where v = degrees of freedom\r<BR>\n" );
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document.write( "The instructions on how to access the tcdf function are provided on the page under where it mentions \"Menu Location\".<BR>\n" );
document.write( "2ND DISTR to access the distribution menu<BR>\n" );
document.write( "5 to select tcdf(, or use arrows.\r<BR>\n" );
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document.write( "So we could say something like <BR>\n" );
document.write( "tcdf(2.837, 99, 25)<BR>\n" );
document.write( "Notice how n = 26 leads to v = n-1 = 26-1 = 25<BR>\n" );
document.write( "Also, recall we're doing a right-tailed test.\r<BR>\n" );
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document.write( "Typing that into the calculator would produce roughly 0.00445028 which rounds to 0.0045\r<BR>\n" );
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document.write( "If you do not have a TI calculator, then you can go for a free option such as this page<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://stattrek.com/online-calculator/t-distribution.aspx\">https://stattrek.com/online-calculator/t-distribution.aspx</a><BR>\n" );
document.write( "Type in 25 as the degrees of freedom and 2.837 as the t score. Leave the last box blank. Then hit the \"calculate\" button.\r<BR>\n" );
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document.write( "The value 0.9955 should show up in that box we left empty.<BR>\n" );
document.write( "This is the approximate area under the T curve to the left of t = 2.837 due to the notation P(T < 2.837), and this applies only when v = 25\r<BR>\n" );
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document.write( "So the area to the right would be 1-0.9955 = 0.0045\r<BR>\n" );
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document.write( "The p-value is smaller than alpha, so we reject the null. It appears the nutritionist's claim is correct. \r<BR>\n" );
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document.write( "Answer: 0.0045<BR>\n" );
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