Obesity and being overweight is caused by excessive adipose tissues, or body fat. Visceral fat, surrounding internal organs, is clearly associated with heart disease and diabetes. Subcutaneous fat, found just below the skin (often in the buttocks and thighs), is not. A study examined the impact of exercise type on visceral and subcutaneous fat. Overweight, sedentary, but otherwise disease-free adults were randomly assigned to 3 exercise regimens for eight months: aerobic training, resistance training, aerobic plus resistance training. All exercise sessions were supervised to ensure correct completion. The subjects' body fat amount was assessed with computed tomography imaging (in cm2) at the beginning and end of the experiment. The study report contains the following information about the visceral fat reduction (in cm2) achieved by the subjects in each group (note that the reduction is indicated as a positive value): Treatment n x s Aerobic training 36 25.7 32 Resistance training 44 8.7 54 Aerobic plus resistance training 35 28.7 35 (A) Calculate the overall mean response x = (round to 2 decimal places)(B) Complete the one-way ANOVA table (round your answer to two decimal places when it applies) Source df S.S. M.S. F Between Groups 2 9435.79 Within Groups C.Total 212313.79
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Obesity and being overweight is caused by excessive adipose tissues, or body fat. Visceral fat, surrounding internal organs, is clearly associated with heart disease and diabetes. Subcutaneous fat, found just below the skin (often in the buttocks and thighs), is not. A study examined the impact of exercise type on visceral and subcutaneous fat. Overweight, sedentary, but otherwise disease-free adults were randomly assigned to 3 exercise regimens for eight months: aerobic training, resistance training, aerobic plus resistance training. All exercise sessions were supervised to ensure correct completion. The subjects' body fat amount was assessed with computed tomography imaging (in cm2) at the beginning and end of the experiment. The study report contains the following information about the visceral fat reduction (in cm2) achieved by the subjects in each group (note that the reduction is indicated as a positive value):
| Treatment | n | x | s |
|---|---|---|---|
| Aerobic training | 36 | 25.7 | 32 |
| Resistance training | 44 | 8.7 | 54 |
| Aerobic plus resistance training | 35 | 28.7 | 35 |
(B) Complete the one-way ANOVA table (round your answer to two decimal places when it applies)
| Source | df | S.S. | M.S. | F |
|---|---|---|---|---|
| Between Groups | 2 | 9435.79 | ||
| Within Groups | ||||
| C.Total | 212313.79 |
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