Question

A cohort study is conducted to assess the effectiveness of a 4-week weight-loss intervention program among overweight men. Sixty participants were randomized into two groups. Group 1 worked with a personal trainer to come up with a physical activity regimen that would best fit their lifestyle, while Group 2 worked with a dietician to co-design a diet program to which the men would most likely adhere. Mean BMI was assessed for each group at the end of the 4 weeks. The results are summarized in the table below:

Physical Activity Program:

Sample Size: 31

Mean BMI (s): 29.1 (6.7)

Diet Program:

Sample Size: 29

Mean BMI (s): 25.9 (8.4)

According to this data, is there evidence at the 0.05 level of the mean BMI for the group that received the physical activity program being significantly higher than the mean BMI for the diet program group?

1. Indicate the null hypothesis:

2. Indicate the alternative/research hypothesis:

3. Indicate the appropriate test statistic:

1. Indicate the decision rule (where “test statistic” = Z or t):

1. Reject H₀ if test statistic > 2.002
2. Reject H₀ if test statistic > 1.645
3. Reject H₀ if test statistic > 1.960
4. Reject H₀ if test statistic > 1.672
5. Some other answer; indicate:

2. Compute and indicate the ratio of sample variances:

1. 0.80
2. 0.64
3. 1.57
4. 1.25
5. Some other answer; indicate:

3. Compute and indicate the pooled estimate of common standard deviation (Sp):

1. Sp = 7.57
2. Sp =57.28
3. Sp =2.74
4. Sp =7.7
5. Some other answer; indicate:

4. Compute the test statistic and indicate the outcome:

1. 0.22
2. 4.52
3. 1.64
4. 6.33
5. Some other answer; indicate:

5. True or false: We have statistically significant evidence at the 5% level to show that the mean BMI for Group 1 is significantly higher than the mean BMI for Group 2.

1. True
2. False

6. Indicate the most accurate p-value associated with the above-mentioned conclusion:

1. p = 0.10
2. p = ns (p > 0.05)
3. p < 0.05
4. p < 0.01
5. Some other answer; indicate:

After observing the results from the first 4 weeks of the study, the researchers of the above-mentioned study decide to conduct a crossover trial in which all 60 of the participants received both the physical activity and diet program. Specifically, the researchers wanted to assess how differing the order of receipt of the programs would affect mean BMI among the groups. Therefore, those participants that received the physical activity program for the first 4 weeks received the diet program for the second 4 weeks. Likewise, those participants that received the diet program first received the physical activity program for the second 4 weeks. If the mean difference in BMI was 6.9 units with a standard deviation of 3.5 units, conduct a hypothesis test to examine if there is a statistically significant difference at the 5% level in mean BMI at the conclusion of the crossover study.

7. Indicate the null hypothesis:
8. Indicate the alternative/research hypothesis:
9. .Indicate the appropriate test statistic:

13. Indicate the decision rule (where “test statistic” = Z or t):

1. Reject H₀ if test statistic < -2.001 or if test statistic > 2.001
2. Reject H₀ if test statistic < -1.960 or if test statistic > 1.960
3. Reject H₀ if -1.671 < test statistic < 1.671
4. Reject H₀ if -1.645 < test statistic < 1.645
5. Some other answer; indicate:

14. Compute the test statistic and indicate the outcome:

1. 118.286
2. 8.19
3. 15.27
4. 63.43
5. Some other answer; indicate:

15. True or false: We have statistically significant evidence at the 5% level to show that the mean difference in BMI between the two groups is significantly different.

1. True
2. False

16. Indicate the most accurate p-value associated with the above-mentioned conclusion:

1. p = not significant
2. p = 0.01
3. p = 0.05
4. p < 0.0001
5. Some other answer; indicate:

Answer 1