1. A speech dialogue system comprising: a data center apparatus that receives speech data of speech sound transmitted from a terminal apparatus, applies a speech recognition process to the speech data to acquire request information expressed by the speech data, acquires answer information for the request information from an information source, creates a scenario including the answer information, creates first synthesized speech data expressing synthesized speech that generates sound of the answer information, transmits the first synthesized speech data created in the creating the first synthesized speech data to the terminal apparatus, and transmits the scenario to the terminal apparatus while the first synthesized speech data is being created in the creating the first synthesized speech data; and the terminal apparatus that acquires input of the speech sound to convert the speech sound to speech data expressing the speech sound, transmits the speech data of the speech sound to the data center apparatus, receives the scenario transmitted from the data center apparatus, creates second synthesized speech data expressing the synthesized speech that generates sound of the answer information included in the received scenario, receives the first synthesized speech data transmitted from the data center apparatus, determines whether the reception of the first synthesized speech data is completed to select one of the first synthesized speech data and the second synthesized speech data based on the determination result, and outputs the synthesized speech expressed by the synthesized speech data selected in the determining, wherein the data center apparatus and the terminal apparatus being connected through a communication network.