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Brums [2.3K]
3 years ago
15

An article reported on the results of an experiment in which half of the individuals in a group of 60 postmenopausal overweight

women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines. The sample mean decrease in body weight for those on the vegan diet was 5.7 kg, and the sample SD was 3.1, whereas for those on the control diet, the sample mean weight loss and standard deviation were 3.9 and 2.7, respectively. Does it appear that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg
Mathematics
1 answer:
slavikrds [6]3 years ago
8 0

Answer:

Step-by-step explanation:

From the given information:

Let's first compute the null and alternative hypothesis

Null hypothesis:

\mathbf{H_o: \mu_1-\mu_2=1}

Alternative hypothesis:

H_a :\mu_1 -\mu_2 > 1

The number of samples is half in a group of 60

i.e

n_1=n_2 = 30

the sample mean for sample 1 \overline x_1 = 5.7

the standard deviation for sample 1 s_1 = 3.1

the sample mean for sample 2 \overline x_2 = 3.9

the standard  deviation for sample 2 s_2 = 2.7

degree of freedom  for this test can be computed by using the formula:

df = \dfrac{\begin {pmatrix} \dfrac{s_1^2}{n_1} + \dfrac{s^2_2}{n_2}   \end {pmatrix}^2  }  {\dfrac{ (\dfrac{s_1^2}{n_1}^2)}{ n_1-1}  + \dfrac{ (\dfrac{s_2^2}{n_2}^2)}{ n_2-1}  }

df = \dfrac{\begin {pmatrix} \dfrac{3.1^2}{30} + \dfrac{2.7^2}{30}   \end {pmatrix}^2  }  {\dfrac{ \begin {pmatrix} \dfrac{3.1^2}{30} \end {pmatrix}^2}{ 30-1}  + \dfrac{ \begin {pmatrix} \dfrac{2.7^2}{30} \end {pmatrix}^2}{ 30-1}  }}

df = 114.68

The test statistics can be computed as follows:

t = \dfrac{ \overline x_1 -\overline x_2- (\mu_1 -\mu_2)}{\sqrt{ \dfrac{s_1^2}{n_1} +\dfrac{s_2^2}{n_2} }}

t = \dfrac{ 5.7-3.9- (1)}{\sqrt{ \dfrac{3.1^2}{30} +\dfrac{2.7^2}{30} }}

t = 1.07

Using the level of significance of 0.1, the P-value for the test statistics at the df of 114.68 is:

P-value = 0.143

Decision rule: To reject the null hypothesis if the level of significance is greater than the p-value.

Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance at 0.1.

Thus, it appears that the true average weight loss for the vegan diet does not exceeds that for the control diet by more than 1 kg.

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A gallon is a British unit which is used for the measurement of liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.

It is given in the question that:-

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Jason's pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.

After 20 minutes the amount of liquid in the tank will be:-

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The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5

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The equation of a line can be represented as follows:

y = mx + b

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Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4

Hence,

perpendicular lines follows the rule below:

m₁m₂ = -1

Hence,

5x - 3y = 4

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Therefore,

y = -3 / 5 x + 13 / 5

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