Can information theory be applied to human interactions and communication? I am not sure if this question is better suited for the computational science SE. 

I learned a bit of Shannon's information theory in a course I took last year. In the class it was defined as the quantitative relaying of information between a signal and a receiver across a medium that introduces noise. In all the examples we explored it was typically defined in terms bits of information that can be quantified and conveyed across the communication channel. Some examples we discussed were data compression, the transfer of DNA from parent cells to daughter cells, and aspects of speech/written words.

Let's say two individuals are in conversation. One speaks a phrase communicating his current state of mind. He then speaks the phrase out loud. The second individual hears this phrase. She then processes it based on her own brain and the way it functions and produces a response. 

Here the signal would be the person speaking the phrase and the receiver would be the person interpreting the phrase. Could we argue that the "noise" in this communication is the subjectivity of the two people? The first person is attempting to convey information that is derived from his particular subjective state and whatever patterns were generated by his brain from his experiences. The second person would have to weight this information against her subjective state and past experiences with the first person. This might introduce "noise" that would affect the intended interpretation of the phrase.

Essentially, my question is with regards to social communication - sometimes you must know the appropriate way to phrase something so that the correct information is conveyed and is not subject to misinterpretation.

Question: Would this be a proper application of information theory?

Note here that I am not talking about the actual information content of the sentences themselves (which may be noisy if imprecise language is used) but the interpretation on the part of the two people in communication.
Information and signal detection theory are commonly applied to cognitive situations. Examples include TSA agents searching for weapons among carry-on bags and sonar operators attempting to discern ships from fish. In addition, information theory itself is highly general, and has been proven to apply across disciplines. So I do think the premise is valid. 

However, the example does not list an application, per se- it simply describes a situation where one might think about coming up with an information-theoric approach. Such an approach would certainly involve a lot of research because there are many confounding factors in communication between humans (not the least of which is the cognitive framework of the receiving individual). You would need to carefully define what is signal, what is noise, and where the boundaries lie. I contend that this would be particularly difficult in the general case.