A major healthcare system wants to reduce job$-$related stress among its employees. In particular, the nursing staff endures a significant amount of pressure due to $12-$hour rotating shifts, required overtime, and challenging job assignments. A few years ago, the hospital's human resources $($HR$)$ department discovered that its nurse turnover rate was much higher than any other professional position at the hospital. Those nurses leaving employment cited work conditions and emotional stress as their main concerns.

To curb this trend, the hospital proactively developed an employee well$-$being program. For over three years, a program manager has sponsored monthly activities specifically designed to improve employee morale and reduce stress. Participation in the program has been strictly voluntary, with a $$50$ cash bonus awarded to all employees who consistently complete the various well$-$being activities every quarter. Nurse participation is specifically being tracked to see if the program has successfully improved job satisfaction and reduced job turnover.

Enrollment in the program has generally increased over time. Sponsored activities are currently developed by a full$-$time athletic trainer, a massage therapist, and a yoga instructor. These professionals also provide individualized services to participants upon request. A full$-$time program coordinator is tasked with administering the program's day$-$to$-$day operations, including the responsibility of expanding employee participation through periodic marketing emails that tout program benefits and upcoming activities. Of course, there are significant internal costs associated with subsidizing this program. Nevertheless, it is widely believed that these expenses are minuscule when compared to the substantial costs associated with replacing employees$$nurses in particular. Accordingly, the program costs and predicted savings are not being considered as part of this initial analysis.

The purpose of this study is to determine if there is a significant relationship between the monthly rate of nurse participation and the nurse attrition rate over the span of $36$ months. Since attrition can be considered a lagging indicator of job satisfaction, the attrition rate is retroactively tied back to each nurse$$s enrollment month. Categorized data for program participation and nurse attrition was extracted and assembled from the program enrollment database and the HR employee database, with the data for analysis shown below.

The hospital executive council is reviewing the program$$s efficacy in reducing nurse attrition through program participation as part of its routine funding plan for the next five years. However, the initial meeting will primarily focus on program efficacy and predictions for future enrollment growth and nurse retention.