Ontario is a world leader in the installation of smart electricity meters on residences. This has allowed the province to charge different rates for electricity at different times of day and has also resulted in the accumulation of a vast database of the amount of electricity (in kilowatt-hours) consumed by each residence during each hour of each day for the past several years. Peak electricity demand in Ontario usually occurs between 3:00 p.m. and 5:00 p.m. in July, when air conditioning use is at a maximum. Hydro One, the largest electricity transmission and distribution company in Ontario, wants to test the effectiveness of its “Peaksaver PLUS” program, which supplies customers with a free thermostat that Hydro One can control remotely to reduce air conditioning use during peak times. They take a random sample of 40 customers with Peaksaver PLUS today and 40 customers without it today to compare their consumption (in kilowatt-hours) of electricity between 3:00 p.m. and 5:00 p.m. in July for the past five years (2 hours × 31 days × 5 years = 310 measurements for each customer).
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) Comparison of electricity consumption between 3:00 p.m. and 4:00 p.m. and electricity consumption between 4:00 p.m. and 5:00 p.m.

b) Analysis of whether 3:00 p.m. to 5:00 p.m. electricity consumption of customers with Peaksaver PLUS is less than that of customers without it.

c) Suppose we want to analyze whether 3:00 p.m. to 5:00 p.m. electricity consumption of customers with Peaksaver PLUS today is less than before they subscribed to it. 

(i) Is this sample of customers satisfactory? 

(ii) If the sample is satisfactory, which statistical test is appropriate?