Q$1.(10$ points$)$ Operations management of a Waterloo, Ontario software company would like to establish a wellness program during the lunch hour to enhance the physical and mental health of its employees. Before introducing the wellness program, operations management must first be convinced that a sufficiently large majority of its employees are not already exercising at lunchtime. Specifically, it plans to initiate the program only if less than $40\%$ of its personnel take time to exercise prior to eating lunch.

To make this decision, operations management has surveyed a random sample of $100$ employees regarding their midday exercise activities. The results of the survey are given in the file Question $1$ file.

Required:

a$.$ Using a $10\%$ significance level, is there sufficient evidence for managers of this organization to initiate a corporate wellness program? Why or why not?

b$.$ Using a $1\%$ significance level, is there sufficient evidence for managers of this organization to initiate a corporate wellness program? Why or why not?