The high electrical conductivity of copper is an important design factor that helps improve the energy efficiency of electric mo
tors. This is important because motors and motor-driven systems are significant consumers of electricity, accounting for 43% - 46% of all global electricity consumption and 69% of all electricity used by industry. Inefficient motors waste electrical energy and are indirect contributors to greenhouse gas emissions. ElectroSpark, Inc. has been developing a new copper die-cast rotor technology specifically for premium efficiency motors, replacing the standard aluminum rotor. There are multiple reasons for doing so, including the possibility that the motor will consume less energy. They designed an experiment to test their idea in a common ¾ Horse power (HP) motor that is normally manufactured with an aluminum rotor. They designed a copper rotor that fit in their ¾ HP motor housing and ran a production line for a day producing the motors. They randomly selected 20 copper-rotor motors from that output and 20 aluminum-rotor motors produced from the same line the day before. These 40 motors were all run for 8 hours a day for 30 days and the energy consumed was measured in total Kilowatt Hours (example data below, using alpha=.05): Copper: 560.145 539.673 556.834 559.873
Aluminium: 564.674 573.912 553.385 574.078
What is the correct hypothesis to test the problem described in this scenario?
A. H0: μD (copper-aluminum) ≥ 0; H1: μD (copper-aluminum) < 0
B. H0: μ_copper – μ_aluminum ≥ 0; H1: μ_copper – μ_aluminum < 0
C. H0: μD (copper-aluminum) ≥ 0; H1: μD (copper-aluminum) > 0
D. H0: μ_copper – μ_Aluminum ≤ 0; H1: μ_copper – μ_aluminum > 0
This is a two sample t-test and not a matched pair t-test
null hypothesis(H0) will be that mean energy consumed by copper rotor motors is greater than or equal to mean energy consumed by aluminium rotor motors
alternate hypothesis(H1) will be that mean energy consumed by copper rotor motors is less than or equal to mean energy consumed by aluminium rotor motors.
So, option D is rejected
The hypothesis will not compare mean of differences of values of energy consumed by copper rotor motor and aluminium rotor motor.
