1. A state detecting apparatus comprising: a processor to execute acquiring utterance data related to uttered speech, computing a plurality of statistical quantities for feature parameters regarding features of the utterance data, creating, on the basis of the plurality of statistical quantities regarding the utterance data and another plurality of statistical quantities regarding reference utterance data based on other uttered speech, pseudo-utterance data having at least one statistical quantity equal to a statistical quantity in the other plurality of statistical quantities, computing a plurality of statistical quantities for synthetic utterance data synthesized on the basis of the pseudo-utterance data and the utterance data, and determining, on the basis of a comparison between statistical quantities of the synthetic utterance data and statistical quantities of the reference utterance data, whether the speaker who produced the uttered speech is in a first state or a second state; and a memory to store the reference utterance data.