A national fitness firm claims that a company may increase employee productivity by implementing one of the firm’s fitness programs at the job site. As evidence of this, the fitness firm reports that one company was able to increase job productivity of a random sample of 30 employees from 57 to 70 (on a scale of 100). The standard deviation of the increases was 7.9. The national fitness firm wants to estimate the mean increase a company could expect after implementing the fitness program.

a) Check the assumptions and conditions for inference.

b) Find a 95% confidence interval.

c) Explain what your interval means in this context.