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.

Name: Is a weight loss program based on exercise just as effective as a prog
Uploaded: 2024-03-20T07:07:12.000Z
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Description: 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 p

Question

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.

Accepted Answer

Given information-
For sample 1 Exercise program-
Average, X1-bar = 28 pounds
Standard deviation, s1…