Partly as a result of a government incentive program, several businesses and residences in Ontario have installed solar panels so as to reduce their electricity bills. The amount of electricity (in kilowatthours) generated by each of these installations is recorded in a database each hour of each day for four years together with the size of installation (in peak kilowatt-hours that could be generated in ideal conditions). Ottawa is a particularly good city for generating solar power because of its year-round clear skies and cold winters (solar panels generate more power at lower temperatures). However, a problem is that snow may accumulate on the panels and prevent them from generating electricity. Snow tends to slide off panels that are steeply sloped but may accumulate on others. 

An installer wants to analyze the effect of snow on electricity generation to figure out whether she should focus on steeply sloped projects in the future to obtain maximum profits over the 25-year life of the panels. She takes a random sample of 30 installations in Ottawa that have a steep slope (745 degrees) and another sample of 30 that have a shallow slope (645 degrees). The total number of installations in Ottawa is 1248. Since some installations are larger than others, she scales the amount of electricity generated by the size of the installation, calculating (kilowatt-hours/peak kilowatt-hours) as a measure of the “effectiveness” of the installation at generating power. 

For the analyses in (a) and (b) below, state (i) the sample you would use from the database; (ii) the hypotheses you would test; (iii) which statistical test you would use, with a reason; and (iv) how you would check the conditions for using that test.

a) Analyze whether the average effectiveness in January of solar installations with a steep slope is higher than for those that have a shallow slope.

b) Compare the amount of electricity generated during three days immediately before the first major snowfall (accumulation 75 cm) of the season with the amount of electricity generated during three days immediately after that first major snowfall.