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A human resource manager for Carver County is evaluating a recent effort to improve the health of the county's firefighters by providing an exercise room in each of the county's firehouses. Their records prior to installing the exercise rooms indicate that the mean weight of all county firefighters is 198 pounds with a standard deviation of 13 pounds. A random sample of 40 firefighters taken six months after the program was implemented revealed that the mean of the sample was 192 pounds. 

Construct a 96% confidence interval for the mean weight of all firefighters six months after the exercise rooms were installed. 

Assume that σ has not changed.  Does it appear that the program is working?

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