Managers of a software development firm have established a wellness program during the lunch hour to enhance the physical and mental health of their employees. Now, they would like to see whether the wellness program has increased the proportion of employees who exercise regularly during the lunch hour. To make this assessment, the managers surveyed a random sample of 100 employees about their noontime exercise habits before the wellness program was initiated. Later, after the program was initiated, another 100 employees were independently chosen and surveyed about their lunchtime exercise habits. The results of these two surveys are given in the file P09_14.xlsx.
a. Find a 95% confidence interval for the difference in the proportions of employees who exercise regularly during their lunch hour before and after the implementation of the corporate wellness program.
b. Does the confidence interval found in part a support the claim that the wellness program has increased the proportion of employees who exercise regularly during the lunch hour? If so, at which levels of significance is this claim supported?
c. Would your results in parts a and b differ if the same 100 employees surveyed before the program were also surveyed after the program? Explain.