Manufacturing and Product Development Most home air conditioners built before 2010 used Freon gas to provide cooling in a typical evaporation cycle. However, Freon, which contains chlorine, was phased out of new equipment by 2010 and will not be used at all by 2020. R-410A, a mixture of difluoromethane and pentafluoroethane, is now the most common refrigerant in the United States. Although an air conditioner is, theoretically, a closed system, units usually lose refrigerant and must be recharged every few years. A random sample of 10,000-BTU air conditioners was obtained, and the amount of refrigerant (in pounds) in each was carefully measured. Each unit was recharged by a technician, and the amount of refrigerant in each was measured after the service. Suppose no assumptions can be made about the shape of the continuous distributions of before and after refrigerant weights.
a. Conduct a sign test to determine whether there is any evidence that the median refrigerant weight before service is less than the median refrigerant weight after service. Use a significance level of a = 0.01.
b. Based on your results, do you believe recharging an air conditioner really results in more refrigerant in the system? Why or why not?