Question 1193195
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Part A


Hypothesis:
H0: mu = 0
H1: mu > 0
The mu refers to the population mean of the differences in weight (actual - ideal)


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.
The inequality sign in the alternative hypothesis tells us we're doing a right-tailed test.


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.
Determining the p-value requires the test statistic.


First let's visit the given info
n = 26 = sample size
xbar = 15.3 = sample mean
s = 27.5 = sample standard deviation
alpha = 0.02 = 2% significance level


Now to compute the test statistic.
t = (xbar - mu)/( s/sqrt(n) )
t = (15.3 - 0)/( 27.5/sqrt(26) )
t = 2.83690903847162 approximately
t = 2.837


Answer: 2.837


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Part B


I recommend a calculator for this. 
You can use a TI (texas instrument) calculator if you have one handy.


If you have a TI calculator, then refer to this documentation page
<a href = "http://tibasicdev.wikidot.com/tcdf">http://tibasicdev.wikidot.com/tcdf</a>
The tcdf function will give the area under the T curve. The format is
tcdf(lower, upper, v)
where v = degrees of freedom


The instructions on how to access the tcdf function are provided on the page under where it mentions "Menu Location".
2ND DISTR to access the distribution menu
5 to select tcdf(, or use arrows.



So we could say something like 
tcdf(2.837, 99, 25)
Notice how n = 26 leads to v = n-1 = 26-1 = 25
Also, recall we're doing a right-tailed test.


Typing that into the calculator would produce roughly 0.00445028 which rounds to 0.0045


If you do not have a TI calculator, then you can go for a free option such as this page
<a href = "https://stattrek.com/online-calculator/t-distribution.aspx">https://stattrek.com/online-calculator/t-distribution.aspx</a>
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.


The value 0.9955 should show up in that box we left empty.
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


So the area to the right would be 1-0.9955 = 0.0045


The p-value is smaller than alpha, so we reject the null. It appears the nutritionist's claim is correct. 


Answer: 0.0045
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