Question

Is a weight loss program based on exercise just as effective as a program based on diet? The 58 overweight people put on a strict one year exercise program lost an average of 22 pounds with a standard deviation of 5 pounds. The 55 overweight people put on a strict one year diet lost an average of 25 pounds with a standard deviation of 10 pounds. What can be concluded at the αα = 0.05 level of significance?

For this study, we should use Select an answer z-test for the difference between two population proportions t-test for the difference between two dependent population means z-test for a population proportion t-test for a population mean t-test for the difference between two independent population means  

The null and alternative hypotheses would be:   

  

H0:H0:  Select an answer μ1 p1   Select an answer > = < ≠   Select an answer μ2 p2   (please enter a decimal)   

H1:H1:  Select an answer p1 μ1   Select an answer > < = ≠   Select an answer p2 μ2   (Please enter a decimal)

The test statistic ? t z   =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is ? ≤ >   αα

Based on this, we should Select an answer accept reject fail to reject   the null hypothesis.

Thus, the final conclusion is that ...

The results are statistically significant at αα = 0.05, 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 = 0.05, so there is sufficient evidence to conclude that the mean weight loss for the 58 participants on the exercise program is different than the mean weight loss for the 55 participants on the diet.

The results are statistically insignificant at αα = 0.05, 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.

The results are statistically insignificant at αα = 0.05, 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.

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

There is a 4.9% chance of a Type I error.

If the sample mean weight loss for the 58 participants on the exercise program is the same as the sample mean weight loss for the 55 participants on the diet and if another 58 participants on the exercise program and 55 participants on the diet are weighed then there would be a 4.9% chance of concluding that the mean weight loss for the 58 participants on the exercise program differs by at least 3 pounds compared to the mean weight loss for the 55 participants on the diet

There is a 4.9% chance that the mean weight loss for the 58 participants on the exercise program differs by at least 3 pounds compared to the mean weight loss for the 55 participants on the diet.

If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 58 and 55 participants on the exercise program and on the diet are observed then there would be a 4.9% chance that the mean weight loss for the 58 participants on the exercise program would differ by at least 3 pounds compared to the mean weight loss for the 55 participants on the diet.

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

There is a 5% 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 58 and 55 participants on the exercise program and on the diet are observed then there would be a 5% chance that we would end up falsely concluding that the sample mean weight loss for these 58 and 55 participants differ from each other.

There is a 5% chance that there is a difference in the population mean weight loss between those on the exercise program and those on the diet.

If the population mean weight loss on the exercise program is equal to the population mean weight loss on the diet and if another 58 and 55 participants on the exercise program and on the diet are observed then there would be a 5% 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

Answer 1

For this study, we should use t-test for the difference between two independent population means  

The null and alternative hypotheses would be:   

H0: μ1 = μ2 ; H1: μ1 ≠ μ2

Test statistic:

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (22 - 25)/√(5²/58 + 10²/55) = -2.000

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 78.4608 = 78

p-value =T.DIST.2T(-2.0003, 78) = 0.0489

The p-value is ≤ α

Based on this, we should reject the null hypothesis.

Thus, the final conclusion is that ...

The results are statistically significant at αα = 0.05, 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.

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Interpret the p-value 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 58 and 55 participants on the exercise program and on the diet are observed then there would be a 4.9% chance that the mean weight loss for the 58 participants on the exercise program would differ by at least 3 pounds compared to the mean weight loss for the 55 participants on the diet.

--

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

There is a 5% chance that there is a difference in the population mean weight loss between those on the exercise program and those on the diet.