Question **10** of the July 2004, Exit Level, Texas Assessment of Knowledge and Skills (TAKS) released Science test reads as follows:

there is a work input of 320 J and a work

output of 80 J?

Out of the 18545 students who took the Grade 11 Exit Level test, the response percentages for answers **F**, **G**, **H**, **J**, and no answer were, respectively, 25%, 53%, 8%, 14%, and 0%. Out of the 806 students who took the Grade 12 Exit Level test, the response percentages were, respectively, 19%, 59%, 7%, 14%, and 0%.

The efficiency of an air conditioner cannot be determined, even roughly, from the given information. The Texas Education Agency made the mistakes of giving credit for answer **G** and of not throwing out question **10**. The TEA wrongly increased the scores of the roughly 10304 students who chose answer **G** and, with respect to the scaled scores that result from thowing out question **10**, wrongly decreased the scaled scores of the remaining roughly 9047 students. The remedy is to remove credit for answer **G**, throw out question **10**, and rescale the test scores based on whatever valid test questions remain.

An air conditioner is driven by work energy, takes in heat energy from the volume being cooled, and outputs heat energy to the exterior of the volume being cooled. According to conservation of energy,

work input + heat input = heat output.

The efficiency of an air conditioner is the ratio of heat input to work input:*^{,} **

heat input

efficiency of an air conditioner
= -------------- .

work input

In choosing answer **G**, the Texas Education Agency apparently mistook "work output" for heat input and failed to recognize that 25% is less than one-tenth the efficiencies of many commonly available air conditioners. For example, Kenmore Model #75051 room air conditioner has an efficiency of about 10.8 (British thermal units)/(Watt hour) = 3.16 = 316%. Room air conditioners built since 1990 are required to have efficiencies of 8.0 (British thermal units)/(Watt hour) = 2.34 = 234% or greater. The TEA apparently also ignored the fact that answers **H** and **J** are better than answer **G**.

____________________

*
This ratio is also called the air conditioner's "coefficient of performance" (COP).

**
The formula

work output
W_{O}

% efficiency = -------------- x 100%
% = ---- x 100,

work input
W_{I}

given in a formula chart on a beginning page of the test, does not apply to air conditioners.