Is a weight loss program based on exercise just as effective as a program based on diet? The 50 overweight people put on a strict one year exercise program lost an average of 28 pounds with a standard deviation of 8 pounds. The 41 overweight people put on a strict one year diet lost an average of 30 pounds with a standard deviation of 5 pounds. What can be concluded at the αα = 0.01 level of significance? 1. Thus, the final conclusion is that ... The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean weight loss for the 50 participants on the exercise program is different than the mean weight loss for the 41 participants on the diet. The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet. 2. Interpret the p-value in the context of the study. There is a 14.94% chance of a Type I error. If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 14.94% chance that the mean weight loss for the 50 participants on the exercise program would differ by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet. There is a 14.94% chance that the mean weight loss for the 50 participants on the exercise program differs by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet. If the sample mean weight loss for the 50 participants on the exercise program is the same as the sample mean weight loss for the 41 participants on the diet and if another 50 participants on the exercise program and 41 participants on the diet are weighed then there would be a 14.94% chance of concluding that the mean weight loss for the 50 participants on the exercise program differs by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet 3. Interpret the level of significance in the context of the study. If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 1% chance that we would end up falsely concluding that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet There is a 1% chance that you are such a beautiful person that you never have to worry about your weight. If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 1% chance that we would end up falsely concluding that the sample mean weight loss for these 50 and 41 participants differ from each other. There is a 1% chance that there is a difference in the population mean weight loss between those on the exercise program and those on the diet.

Is a weight loss program based on exercise just as effective as a program based on diet? The 50 overweight people put on a strict one year exercise program lost an average of 28 pounds with a standard deviation of 8 pounds. The 41 overweight people put on a strict one year diet lost an average of 30 pounds with a standard deviation of 5 pounds. What can be concluded at the αα = 0.01 level of significance? 1. Thus, the final conclusion is that ... The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean weight loss for the 50 participants on the exercise program is different than the mean weight loss for the 41 participants on the diet. The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet. 2. Interpret the p-value in the context of the study. There is a 14.94% chance of a Type I error. If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 14.94% chance that the mean weight loss for the 50 participants on the exercise program would differ by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet. There is a 14.94% chance that the mean weight loss for the 50 participants on the exercise program differs by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet. If the sample mean weight loss for the 50 participants on the exercise program is the same as the sample mean weight loss for the 41 participants on the diet and if another 50 participants on the exercise program and 41 participants on the diet are weighed then there would be a 14.94% chance of concluding that the mean weight loss for the 50 participants on the exercise program differs by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet 3. Interpret the level of significance in the context of the study. If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 1% chance that we would end up falsely concluding that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet There is a 1% chance that you are such a beautiful person that you never have to worry about your weight. If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 1% chance that we would end up falsely concluding that the sample mean weight loss for these 50 and 41 participants differ from each other. There is a 1% chance that there is a difference in the population mean weight loss between those on the exercise program and those on the diet.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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1. Thus, the final conclusion is that ...

The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet.
The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet.
The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean weight loss for the 50 participants on the exercise program is different than the mean weight loss for the 41 participants on the diet.
The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet.

2. Interpret the p-value in the context of the study.

There is a 14.94% chance of a Type I error.
If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 14.94% chance that the mean weight loss for the 50 participants on the exercise program would differ by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet.
There is a 14.94% chance that the mean weight loss for the 50 participants on the exercise program differs by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet.
If the sample mean weight loss for the 50 participants on the exercise program is the same as the sample mean weight loss for the 41 participants on the diet and if another 50 participants on the exercise program and 41 participants on the diet are weighed then there would be a 14.94% chance of concluding that the mean weight loss for the 50 participants on the exercise program differs by at least 2 pounds compared to the mean weight loss for the 41 participants on the diet

3. Interpret the level of significance in the context of the study.

If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 1% chance that we would end up falsely concluding that the population mean weight loss on the exercise program is different than the population mean weight loss on the diet
There is a 1% chance that you are such a beautiful person that you never have to worry about your weight.
If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 50 and 41 participants on the exercise program and on the diet are observed then there would be a 1% chance that we would end up falsely concluding that the sample mean weight loss for these 50 and 41 participants differ from each other.
There is a 1% chance that there is a difference in the population mean weight loss between those on the exercise program and those on the diet.

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 + ...

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