Health$-$care costs in the United States and Canada are concerns for citizens and politicians. The question is$,$ How can we devise a system wherein people$$s medical bills are covered but individuals attempt to reduce costs? An American company has come up with a possible solution. Golden Rule is an insurance company in Indiana with $1,300$ employees. The company offered its employees a choice of programs. One choice was a medical savings account $($MSA$)$ plan. Here$$s how it works. To ensure that a major illness or accident does not financially destroy an employee, Golden Rule offers catastrophic insurance$$a policy that covers all expenses above $$2,000$ per year. At the beginning of the year, the company deposits $$1,000($for a single employee$)$ and $$2,000($for an employee with a family$)$ into the MSA. For minor expenses, the employee pays from his or her MSA. As an incentive for the employee to spend wisely, any money left in the MSA at the end of the year can be withdrawn by the employee. To determine how well it works, a random sample of employees who opted for the medical savings account plan was compared to employees who chose the regular plan. At the end of the year, the medical expenses for each employee were recorded. Critics of MSA say that the plan leads to poorer health care, and as a result employees are less likely to be in excellent health. To address this issue, each employee was examined. The results of the examination were recorded where and $1=$excellent health and $2=$not in excellent health. Use a $5\%$ significance level.

a$)$ Can we infer from these data that MSA is effective in reducing costs? $(10$ Points$)$

b$)$ Can we infer that the critics of MSA are correct? $(10$ Points$)$