Question

Deal with an experiment to study the effects of financial incentives to quit smoking. 19 Smokers at a company were invited to participate in a smoking cessation program and randomly assigned to one of two groups. Those in the Reward group would get a cash award if they stopped smoking for six months. Those in the Deposit group were asked to deposit some money which they would get back along with a substantial bonus if they stopped smoking. The random assignment at the start of the experiment put 1017 smokers in the Reward group and 914 of them agreed to participate. However, only 146 of the 1053 smokers assigned to the Deposit group agreed to participate (since they had to risk some of their own money). Set up a two-way table and compare the participation rates between subjects assigned to the two treatment groups.

Short answer

Using the calculations, the participation rate of the Reward group is approximately 89.87%, and for the Deposit group, it's approximately 13.87%. Thus, the Reward group has a significantly higher participation than the Deposit group in the smoking cessation program.

Step-by-step solution

Establish the Two-Way Table

A two-way table is set up with two categories: 'Invited' and 'Agreed to Participate'. These categories will be analysed for each group, the Reward group and the Deposit group. The given numbers are inserted appropriately into this table. The number invited and the number agreed to participate in the Reward group was 1017 and 914, respectively. In the Deposit group, these numbers were 1053 and 146, respectively.

Calculate the Participation Rates

Calculate the participation rate by dividing the number of those who agreed to participate by the initial number of individuals invited in each group. In this case, it would be \( \frac{914}{1017} \) for the Reward group and \( \frac{146}{1053} \) for the Deposit group, and then each multiplied by 100 to get the percentage.

Compare the Participation Rates

The final step involves comparing the results obtained from the calculations in Step 2. This comparison provides an idea of the effectiveness of the two treatment methods in terms of participation rates.