Physical activity of obese young adults. Refer to the International Journal of Obesity (Ja...

Physical activity of obese young adults. Refer to the International Journal of Obesity (Jan. 2007) study of the physical activity of obese young adults, presented in Exercise.

Physical activity of obese young adults. In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject ( International Journal of Obesity , January 2007). The study revealed that the overall physical activity of obese young adults has a mean of μ = 320 cpm and a standard deviation of σ = 100 cpm. (In comparison, the mean for young adults of normal weight is 540 cpm.) In a random sample of n = 100 obese young adults, consider the sample mean counts per minute,

a. Describe the sampling distribution of

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b. What is the probability that the mean overall physical activity level of the sample is between 300 and 310 cpm?

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c. What is the probability that the mean overall physical activity level of the sample is greater than 360 cpm?

For two groups of young adults—13 obese and 15 of normal weight—researchers recorded the total number of registered movements (counts) of each young adult over a period of time. Baseline physical activity was then computed as the number of counts per minute (cpm). Four years later, physical activity measurements were taken again—called physical activity at follow-up.

a. For the 13 obese young adults, the researchers reported a correlation of r = .50 between baseline and follow-up physical activity, with an associated p -value of .07. Give a practical interpretation of this correlation coefficient and p -value.

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b. Refer to part a. Construct a scatterplot of the 13 data points that would yield a value of r = .50.

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c. For the 15 young adults of normal weight, the researchers reported a correlation of r = -.12 between baseline and follow-up physical activity, with an associated p -value of .66. Give a practical interpretation of this correlation coefficient and p -value.

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d. Refer to part c. Construct a scatterplot of the 15 data points that would yield a value of r = -12.