Home solar heating systems can be categorized into two groups, passive solar heating systems and active solar heating systems. In a passive solar heating system, the house itself is a solar energy collector, whereas in an active solar heating system, elaborate mechanical equipment is used to convert the sun’s rays into heat. Consider the difference between the proportions of passive solar and active solar heating systems that require less than 200 gallons of oil per year in fuel consumption. Independent random samples of 50 passive and 50 active solar-heated homes are selected and the numbers that required less than 200 gallons of oil last year are noted, with the results given in the table on the next page. Is there evidence of a difference between the proportions of passive and active solarheated homes that required less than 200 gallons of oil in fuel consumption last year? Test at a level of significance of α = .02.

 

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Passive Solar Active Solar Number of Homes 50 50 Number That Required Less Than 200 Gallons of Oil Last Year 37 46