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Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:


To test it, use F-test statistics and compare variances of each treatment.
Calculate F-value:



F = 1.8356
The <u>critical value of F</u> is given by a F-distribution table with:
degree of freedom (row): 20 - 1 = 19
degree of freedom (column): 20 - 1 = 19
And a significance level: α = 0.05
= 2.2341
Comparing both values of F:
1.856 < 2.2341
i.e. F-value calculated is less than F-value of the table.
Therefore, failed to reject
, meaning there is <u>no sufficient data to support the claim</u> that sham treatment have pain reductions which vary more than for those using magnets treatment.
The line integral along the given positively oriented curve is -216π. Using green's theorem, the required value is calculated.
<h3>What is green's theorem?</h3>
The theorem states that,

Where C is the curve.
<h3>Calculation:</h3>
The given line integral is

Where curve C is a circle x² + y² = 4;
Applying green's theorem,
P = 9y³; Q = -9x³
Then,



⇒ 
Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as
0 ≤ r ≤ 2; and 0 ≤ θ ≤ 2π
Then the integral becomes

⇒ 
⇒ 
⇒ 
⇒ 
⇒ ![-108[2\pi - 0]](https://tex.z-dn.net/?f=-108%5B2%5Cpi%20-%200%5D)
⇒ -216π
Therefore, the required value is -216π.
Learn more about green's theorem here:
brainly.com/question/23265902
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Answer:
15cd(1 + 2cd)
Step-by-step explanation:
greatest common factor is 15cd
