Elements of Statistical Inference Researchers are interested in whether giving individuals temporary financial incentives can induce them to exercise more and lead to the creation of long-lasting habits. To study this question, researchers placed 118 participants into two randomly assigned groups: treatment and control. The treatment group will get a financial incentive to attend the gym more often and the control group will not and then they will compare a variety of outcomes across groups at the end of the experiment. The dummy variable treatment will keep track of which participants are in which group and takes the value of 1 if the individual is in the treatment group and 0 otherwise. If treatment is truly randomly assigned, we shouldn't expect systematic differences across groups in predetermined characteristics. However, it is good research practice to show that the characteristics of each group look 'balanced' and consistent with random assignment. For instance, we might investigate the extent to which there are any pre-existing differences in exercise habits across the groups before the experiment. Consider the following information on gym visits for the month prior to the experiment. Gym Visits (in the month prior to the start of the experiment) Control Group (treatment=0) Treatment Group (treatment=1) Mean 2.48 1.84 Standard deviation 3.79 3.30 Observations 58 60 From this table we can see that the treatment-control difference is -0.64. In other words, the treatment group averaged 0.64 fewer gym visits in the month prior to the start of the experiment. Is this kind of difference normal? In the next series of questions, you will use the above information to (eventually) construct a 95% confidence interval estimate of the treatment-control difference as well as conduct a significance test of the difference. 1. What is the average of the variable treatment in this sample? (to at least 2 decimal places) Hint: You can figure it out based on the number of observations in each group. 2. What is the standard deviation of the variable treatment in this sample? (to at least 2 decimal places) 3. Calculate the approximate standard error of the treatment-control difference in average gym visits using the available information. (to at least 2 decimal places) 4. Construct an approximate 95% confidence interval estimate of the treatment-control difference. What is the lower bound? (to at least 1 decimal place) 5. What is the upper bound of the 95% confidence interval? (to at least 1 decimal place) 6. Calculate the test-statistic (t) for the null hypothesis that there is no systematic difference between treatment and control groups in gym visits per month prior to the start of the experiment. (round to at least 1 decimal place) 7. Based on this information, do you expect the p-value of this test will be a. greater than 0.05 b. less than 0.05
Elements of Statistical Inference
Researchers are interested in whether giving individuals temporary financial incentives can induce them to exercise more and lead to the creation of long-lasting habits. To study this question, researchers placed 118 participants into two randomly assigned groups: treatment and control. The treatment group will get a financial incentive to attend the gym more often and the control group will not and then they will compare a variety of outcomes across groups at the end of the experiment. The dummy variable treatment will keep track of which participants are in which group and takes the value of 1 if the individual is in the treatment group and 0 otherwise.
If treatment is truly randomly assigned, we shouldn't expect systematic differences across groups in predetermined characteristics. However, it is good research practice to show that the characteristics of each group look 'balanced' and consistent with random assignment. For instance, we might investigate the extent to which there are any pre-existing differences in exercise habits across the groups before the experiment. Consider the following information on gym visits for the month prior to the experiment.
Gym Visits (in the month prior to the start of the experiment)
| Control Group (treatment=0) | Treatment Group (treatment=1) | |
| Mean | 2.48 | 1.84 |
| Standard deviation | 3.79 | 3.30 |
| Observations | 58 | 60 |
From this table we can see that the treatment-control difference is -0.64. In other words, the treatment group averaged 0.64 fewer gym visits in the month prior to the start of the experiment. Is this kind of difference normal?
In the next series of questions, you will use the above information to (eventually) construct a 95% confidence
1.
What is the average of the variable treatment in this sample? (to at least 2 decimal places)
Hint: You can figure it out based on the number of observations in each group.
2.
What is the standard deviation of the variable treatment in this sample? (to at least 2 decimal places)
3.
Calculate the approximate standard error of the treatment-control difference in average gym visits using the available information. (to at least 2 decimal places)
4.
Construct an approximate 95% confidence interval estimate of the treatment-control difference. What is the lower bound? (to at least 1 decimal place)
5.
What is the upper bound of the 95% confidence interval? (to at least 1 decimal place)
6.
Calculate the test-statistic (t) for the null hypothesis that there is no systematic difference between treatment and control groups in gym visits per month prior to the start of the experiment. (round to at least 1 decimal place)
7.
Based on this information, do you expect the p-value of this test will be
a. greater than 0.05
b. less than 0.05
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