The director of an obesity clinic in a large northwestern city believes that drinking soft drinks contribute to obesity in children. To determine whether a relationship exists between these two variables, she conducts the following pilot study. Eight- 12-year-old male volunteers are randomly selected from children attending a local junior high school. Parents of the children are asked to monitor the number of soft drinks consumed by their child over a one week period. The children are weighed at the end of the week and their weights converted into body mass index (BMI) values. The BMI is a common index used to measure obesity and takes into account both height and weight. An individual is considered obese if they have a BMI value 30. The following data or collected: child. # of soft drinks consumed BMI 1 3 20 2 1 18 3 14 32 4 7 24 5 21 35 6 5 19 7 25 38 8 9 30 what is the the alternative and null hypotheses? what is the mean and standard deviation for each group? what is the result and conclusion? clear indication of the hypothesis test being conducted and statistic?

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Description: The director of an obesity clinic in a large northwestern city believes that drinking soft drinks contribute to obesity in children. To determine whether a relationship exists between these two variables, she conducts the following pilot study. Eight

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The director of an obesity clinic in a large northwestern city believes that drinking soft drinks contribute to obesity in children. To determine whether a relationship exists between these two variables, she conducts the following pilot study. Eight- 12-year-old male volunteers are randomly selected from children attending a local junior high school. Parents of the children are asked to monitor the number of soft drinks consumed by their child over a one week period. The children are weighed at the end of the week and their weights converted into body mass index (BMI) values. The BMI is a common index used to measure obesity and takes into account both height and weight. An individual is considered obese if they have a BMI value 30. The following data or collected:

child. # of soft drinks consumed BMI

1 3 20

2 1 18

3 14 32

4 7 24

5 21 35

6 5 19

7 25 38

8 9 30

what is the the alternative and null hypotheses?
what is the mean and standard deviation for each group?

what is the result and conclusion?

clear indication of the hypothesis test being conducted and statistic?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

Use the given data to form excel table:

	X	Y	X*Y	X*X	Y*Y
	3	20	60	9	400
	1	18	18	1	324
	14	32	448	196	1024
	7	24	168	49	576
	21	35	735	441	1225
	5	19	95	25	361
	25	38	950	625	1444
	9	30	270	81	900
Sum	85	216	2744	1427	6254
Average	10.625	27
S.D	8.6510	7.7644

$\begin{array}{rcl} Mean (X) & = & \frac{\sum x}{n} \\ = & \frac{85}{8} \\ = & 10.625 \end{array}$

$\begin{array}{rcl} Mean (Y) & = & \frac{\sum y}{n} \\ = & \frac{216}{8} \\ = & 27 \end{array}$

$\begin{array}{rcl} S . D (X) & = & \sqrt{\frac{{(x - \bar{x})}^{2}}{n - 1}} \\ = & 8.6510 \end{array}$

$\begin{array}{rcl} S . D (Y) & = & \sqrt{\frac{{(y - \bar{y})}^{2}}{n - 1}} \\ = & 7.7644 \end{array}$

The correlation for the given data is given as:

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